Updated on 2026/04/30

写真a

 
OGITA, Takeshi
 
Affiliation
Faculty of Science and Engineering, School of Fundamental Science and Engineering
Job title
Professor
Degree
博士（情報科学） ( 2003.03 早稲田大学 )
Homepage URL
https://ogilab.w.waseda.jp/ogita/

Research Experience

  • 2023.04
    -
    Now

    Waseda University   Department of Applied Mathematics, Faculty of Science and Engineering   Professor

  • 2018.04
    -
    2023.03

    Tokyo Woman's Christian University   Division of Mathematical Sciences, School of Arts and Sciences

  • 2010.04
    -
    　

    Tokyo Woman's Christian University   School of Arts and Sciences, Division of Mathematical Sciences

  • 2009.04
    -
    　

    Tokyo Woman's Christian University   School of Arts and Sciences, Division of Mathematical Sciences

  • 2008.04
    -
    　

    Tokyo Woman's Christian University   Department of Mathematics, College of Arts and Sciences

  • 2005.02
    -
    　

    科学技術振興機構 CREST研究員

  • 2003.04
    -
    　

    Waseda University   Graduate School of Science and Engineering

  • 2001.04
    -
    　

    Waseda University   School of Education

▼display all

Education Background

  • 2001.04
    -
    2003.03

    Waseda University   Graduate School of Science and Engineering  

  • 1999.04
    -
    2001.03

    Waseda University   Graduate School of Science and Engineering  

  • 1995.04
    -
    1999.03

    Waseda University   School of Education  

Committee Memberships

  • 2010
    -
    　

    -: 日本応用数理学会 評議員

  • 2008
    -
    　

    -: JSIAM Letters, Associate Editor

  • 2008
    -
    　

    -: 日本応用数理学会 学会誌編集委員

  • 2005
    -
    2007

    : 電子情報通信学会 基礎・境界ソサイエティ運営委員会 事業担当幹事（役員）

  • 　
    　
    　

    日本応用数理学会  正会員

Professional Memberships

  • 　
    　
    　

    日本応用数理学会

  • 　
    　
    　

    SIAM

Research Areas

  • Computational science   Verified Numerical Computations

Research Interests

  • 高精度数値計算

  • 精度保証付き数値計算

  • 数値線形代数

Awards

  • 日本応用数理学会論文賞

    2006  

  • 小野梓記念学術賞

    2003  

 

Papers

  • Extension of accurate numerical algorithms for matrix multiplication based on error-free transformation

    Katsuhisa Ozaki, Daichi Mukunoki, Takeshi Ogita

    Japan Journal of Industrial and Applied Mathematics    2024.10

    DOI

    Scopus

    1
    Citation
    (Scopus)

  • Infinite-Precision Inner Product and Sparse Matrix-Vector Multiplication Using Ozaki Scheme with Dot2 on Manycore Processors

    Daichi Mukunoki, Katsuhisa Ozaki, Takeshi Ogita, Toshiyuki Imamura

    Parallel Processing and Applied Mathematics     40 - 54  2023.04

    DOI

    Scopus

    3
    Citation
    (Scopus)

  • Acceleration of Iterative Refinement for Symmetric Eigenvalue Decomposition

      15 ( 1 ) 1 - 12  2022.07

  • Generation of test matrices with specified eigenvalues using floating-point arithmetic

    Katsuhisa Ozaki, Takeshi Ogita

    NUMERICAL ALGORITHMS   90 ( 1 ) 241 - 262  2022.05

    DOI

    Scopus

    1
    Citation
    (Scopus)

  • Accurate Matrix Multiplication on Binary128 Format Accelerated by Ozaki Scheme

    Daichi Mukunoki, Katsuhisa Ozaki, Takeshi Ogita, Toshiyuki Imamura

    ACM International Conference Proceeding Series    2021.08

    DOI

    Scopus

    8
    Citation
    (Scopus)

  • Verified Numerical Computations for Large-Scale Linear Systems

    Katsuhisa Ozaki, Takeshi Terao, Takeshi Ogita, Takahiro Katagiri

    APPLICATIONS OF MATHEMATICS   66 ( 2 ) 269 - 285  2021.04

    DOI

    Scopus

    2
    Citation
    (Scopus)

  • Efficient Parallel Multigrid Methods on Manycore Clusters with Double/Single Precision Computing.

    Kengo Nakajima, Takeshi Ogita, Masatoshi Kawai

    IEEE International Parallel and Distributed Processing Symposium Workshops     760 - 769  2021

    DOI

    Scopus

    1
    Citation
    (Scopus)

  • Conjugate Gradient Solvers with High Accuracy and Bit-wise Reproducibility between CPU and GPU using Ozaki scheme.

    Daichi Mukunoki, Katsuhisa Ozaki, Takeshi Ogita, Roman Iakymchuk

        100 - 109  2021

    DOI

    Scopus

    8
    Citation
    (Scopus)

  • Performance and energy consumption of accurate and mixed-precision linear algebra kernels on GPUs.

    Daichi Mukunoki, Takeshi Ogita

    J. Comput. Appl. Math.   372   112701 - 112701  2020.07  [Refereed]

    DOI

    Scopus

    14
    Citation
    (Scopus)

  • Modified error bounds for approximate solutions of dense linear systems

    Atsushi Minamihata, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi

    Journal of Computational and Applied Mathematics   369  2020.05

    DOI

    Scopus

    2
    Citation
    (Scopus)

  • Iterative refinement for singular value decomposition based on matrix multiplication

    Takeshi Ogita, Kensuke Aishima

    Journal of Computational and Applied Mathematics   369  2020.05

    DOI

    Scopus

    14
    Citation
    (Scopus)

  • An a posteriori verification method for generalized Hermitian eigenvalue problems in large-scale electronic state calculations

    Takeo Hoshi, Takeshi Ogita, Katsuhisa Ozaki, Takeshi Terao

    J. Comp. Appl. Math.   376   112830/1 - 13  2020.02  [Refereed]

    DOI

    Scopus

    5
    Citation
    (Scopus)

  • DGEMM Using Tensor Cores, and Its Accurate and Reproducible Versions.

    Daichi Mukunoki, Katsuhisa Ozaki, Takeshi Ogita, Toshiyuki Imamura

        230 - 248  2020

    DOI

    Scopus

    25
    Citation
    (Scopus)

  • The Essentials of verified numerical computations, rounding error analyses, interval arithmetic, and error-free transformations

    Katsuhisa Ozaki, Takeshi Ogita

    IEICE NONLINEAR THEORY AND ITS APPLICATIONS   11 ( 3 ) 279 - 302  2020

    DOI

  • LU-Cholesky QR algorithms for thin QR decomposition.

    Takeshi Terao, Katsuhisa Ozaki, Takeshi Ogita

    Parallel Comput.   92   102571 - 102571  2020

    DOI

    Scopus

    26
    Citation
    (Scopus)

  • Iterative refinement for symmetric eigenvalue decomposition II: clustered eigenvalues

    Takeshi Ogita, Kensuke Aishima

    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS   36 ( 2 ) 435 - 459  2019.07

    DOI

    Scopus

    18
    Citation
    (Scopus)

  • Reproducible BLAS Routines with Tunable Accuracy Using Ozaki Scheme for Many-Core Architectures.

    Daichi Mukunoki, Takeshi Ogita, Katsuhisa Ozaki

        516 - 527  2019

    DOI

    Scopus

    15
    Citation
    (Scopus)

  • Iterative refinement for symmetric eigenvalue decomposition

    Takeshi Ogita, Kensuke Aishima

    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS   35 ( 3 ) 1007 - 1035  2018.11

    DOI

    Scopus

    23
    Citation
    (Scopus)

  • Threaded Accurate Matrix-Matrix Multiplications with Sparse Matrix-Vector Multiplications.

    Shuntaro Ichimura, Takahiro Katagiri, Katsuhisa Ozaki, Takeshi Ogita, Toru Nagai

        1093 - 1102  2018

    DOI

    Scopus

    9
    Citation
    (Scopus)

  • Generation of linear systems with specified solutions for numerical experiments

    Katsuhisa Ozaki, Takeshi Ogita

    Reliable Computing   25   148 - 167  2017

  • Acceleration of a preconditioning method for ill-conditioned dense linear systems by use of a BLAS-based method

    Yuka Kobayashi, Takeshi Ogita, Katsuhisa Ozaki

    Reliable Computing   25   15 - 23  2017

  • Error-free transformation of matrix multiplication with a posteriori validation

    Katsuhisa Ozaki, Takeshi Ogita, Shin'ichi Oishi

    NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS   23 ( 5 ) 931 - 946  2016.10  [Refereed]

    DOI

    Scopus

    7
    Citation
    (Scopus)

  • Simple floating-point filters for the two-dimensional orientation problem

    Katsuhisa Ozaki, Florian Buenger, Takeshi Ogita, Shin'ichi Oishi, Siegfried M. Rump

    BIT NUMERICAL MATHEMATICS   56 ( 2 ) 729 - 749  2016.06  [Refereed]

    DOI

    Scopus

    5
    Citation
    (Scopus)

  • Improvement of error-free splitting for accurate matrix multiplication

    Katsuhisa Ozaki, Takeshi Ogita, Shin'ichi Oishi

    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS   288   127 - 140  2015.11  [Refereed]

    DOI

    Scopus

    1
    Citation
    (Scopus)

  • Accelerating interval matrix multiplication by mixed precision arithmetic

    Ozaki Katsuhisa, Ogita Takeshi, Bünger Florian, Oishi Shin'ichi

    Nonlinear Theory and Its Applications, IEICE   6 ( 3 ) 364 - 376  2015

    　View Summary

    This paper is concerned with real interval arithmetic. We focus on interval matrix multiplication. Well-known algorithms for this purpose require the evaluation of several point matrix products to compute one interval matrix product. In order to save computing time we propose a method that modifies such known algorithm by partially using low-precision floating-point arithmetic. The modified algorithms work without significant loss of tightness of the computed interval matrix product but are about 30% faster than their corresponding original versions. The negligible loss of accuracy is rigorously estimated.

    DOI CiNii

  • Special section on recent progress in verified numerical computations

    Ogita Takeshi, Ozaki Katsuhisa, M. Rump Siegfried

    Nonlinear Theory and Its Applications, IEICE   6 ( 3 ) 340 - 340  2015

    DOI CiNii

  • A fast and efficient algorithm for solving ill-conditioned linear systems

    Kobayashi Yuka, Ogita Takeshi

    JSIAM Letters   7   1 - 4  2015

    　View Summary

    In this paper, a fast and accurate algorithm for solving ill-conditioned linear systems is proposed. The proposed algorithm is based on a preconditioned technique using a result of an LU factorization, which requires less computational cost than a previous method using an approximate inverse. The algorithm can provide accurate numerical solutions for ill-conditioned problems beyond the limit of the working precision. Results of numerical experiments are presented for confirming the effectiveness of the proposed algorithm.

    DOI CiNii

  • Improved error bounds for linear systems with H-matrices

    Atsushi Minamihata, Kouta Sekine, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi

    IEICE NONLINEAR THEORY AND ITS APPLICATIONS   6 ( 3 ) 377 - 382  2015

    DOI

  • Generalization of error-free transformation for matrix multiplication and its application

    Ozaki Katsuhisa, Ogita Takeshi, Oishi Shin'ichi, Rump Siegfried M.

    Nonlinear Theory and Its Applications, IEICE   4 ( 1 ) 2 - 11  2013

    　View Summary

    This paper is concerned with accurate numerical algorithms for matrix multiplication. Recently, an error-free transformation from a product of two floating-point matrices into an unevaluated sum of floating-point matrices has been developed by the authors. Combining this technique and accurate summation algorithms, new algorithms for accurate matrix multiplication could be investigated. In this paper, it is mentioned that the previous work is not the unique way to achieve an error-free transformation and the constraint of the error-free transformation is clarified. For the application, a new algorithm is developed reducing the number of matrix products compared to the previous algorithm.

    DOI CiNii

  • Fast verified solutions of sparse linear systems with H-matrices

    A. Minamihata, K. Sekine, T. Ogita, S. Oishi

    Reliable Computing   19 ( 2 ) 127 - 141  2013

  • Verified Numerical Computations for Solutions of Linear Systems(<Special Feature>Reliability in numerical simulation)

    Ogita Takeshi

    Journal of the Japan Society for Simulation Technology   31 ( 3 ) 139 - 143  2012.09

    CiNii

  • A robust algorithm for geometric predicate by error-free determinant transformation

    Katsuhisa Ozaki, Takeshi Ogita, Shin'ichi Oishi

    INFORMATION AND COMPUTATION   216   3 - 13  2012.07  [Refereed]

    DOI

    Scopus

    3
    Citation
    (Scopus)

  • Accurate and verified numerical computation of the matrix determinant

    Takeshi Ogita

    International Journal of Reliability and Safety   6 ( 1-3 ) 242 - 254  2012

    DOI

    Scopus

    2
    Citation
    (Scopus)

  • Introduction of CREST Program : Establishment of Foundations of Verified Numerical Computations for Nonlinear Systems and Error-free Algorithms in Computational Engineering(Laboratories)

    Oishi Shin'ichi, Ogita Takeshi, Ozaki Katsuhisa

    Bulletin of the Japan Society for Industrial and Applied Mathematics   22 ( 3 ) 216 - 218  2012

    DOI CiNii

  • Accurate and robust inverse Cholesky factorization

    Ogita Takeshi, Oishi Shin'ichi

    Nonlinear Theory and Its Applications, IEICE   3 ( 1 ) 103 - 111  2012

    　View Summary

    In this paper, an algorithm for an accurate matrix factorization based on Cholesky factorization for extremely ill-conditioned matrices is proposed. The Cholesky factorization is widely used for solving a system of linear equations whose coefficient matrix is symmetric and positive definite. However, it sometimes breaks down by the presence of an imaginary root due to the accumulation of rounding errors, even if the matrix is actually positive definite. To overcome this, a completely stable algorithm named inverse Cholesky factorization is investigated, which never breaks down as long as the matrix is symmetric and positive definite. The proposed algorithm consists of standard numerical algorithms and an accurate algorithm for dot products. Moreover, it is shown that the algorithm can also verify the positive definiteness of a given real symmetric matrix. Numerical results are presented for illustrating the performance of the proposed algorithms.

    DOI CiNii

  • Matrix Multiplication with Guaranteed Accuracy by Level 3 BLAS

    Katsuhisa Ozaki, Takeshi Ogita, Shin'ichi Oishi

    INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2009 (ICCMSE 2009)   1504   1128 - 1133  2012  [Refereed]

    DOI

    Scopus

  • Robust Computation of Determinant

    Takeshi Ogita

    INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2009 (ICCMSE 2009)   1504   1119 - 1123  2012  [Refereed]

    DOI

    Scopus

    1
    Citation
    (Scopus)

  • Fast algorithms for floating-point interval matrix multiplication

    Katsuhisa Ozaki, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi

    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS   236 ( 7 ) 1795 - 1814  2012.01  [Refereed]

    DOI

    Scopus

    8
    Citation
    (Scopus)

  • Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications

    Katsuhisa Ozaki, Takeshi Ogita, Shin'ichi Oishi, Siegfried M. Rump

    NUMERICAL ALGORITHMS   59 ( 1 ) 95 - 118  2012.01  [Refereed]

    DOI

    Scopus

    54
    Citation
    (Scopus)

  • A note on a verified automatic integration algorithm

    Naoya Yamanaka, Masahide Kashiwagi, Shin'ichi Oishi, Takeshi Ogita

    Reliable Computing   15 ( 2 ) 156 - 167  2011.06

  • Research Group on Verified Numerical Simulations(Introduction of Research Groups of JSST)

    Oishi Shinich, Ogita Takeshi

    Journal of the Japan Society for Simulation Technology   30 ( 1 ) 43 - 45  2011.04

    CiNii

  • Tight and efficient enclosure of matrix multiplication by using optimized BLAS

    Katsuhisa Ozaki, Takeshi Ogita, Shin'ichi Oishi

    NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS   18 ( 2 ) 237 - 248  2011.03  [Refereed]

    DOI

    Scopus

    11
    Citation
    (Scopus)

  • An algorithm for automatically selecting a suitable verification method for linear systems

    Katsuhisa Ozaki, Takeshi Ogita, Shin&apos;ichi Oishi

    NUMERICAL ALGORITHMS   56 ( 3 ) 363 - 382  2011.03  [Refereed]

    DOI

    Scopus

    3
    Citation
    (Scopus)

  • Tight Enclosure of Matrix Multiplication without Directed Rounding

    Ozaki Katsuhisa, Ogita Takeshi, Oishi Shin'ichi

    Bulletin of the Japan Society for Industrial and Applied Mathematics   21 ( 3 ) 186 - 196  2011

    　View Summary

    This paper is concerned with interval arithmetic, especially, an enclosure of a matrix product is focused on. Using level 3 operations of matrix computations, an algorithm outputting a tight enclosure for matrix multiplication is proposed. Most of the algorithms for this purpose require switches of rounding modes defined in the IEEE standard 754. However some programing enviroments have not supported them. Our proposed method demands only rounding-to-nearest mode, so that it is very portable.

    DOI CiNii

  • Fast verification for all eigenpairs in symmetric positive definite generalized eigenvalue problems

    Shinya Miyajima, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi

    Reliable Computing   14   24 - 45  2010.06

  • A fast verified automatic integration algorithm using double exponential formula

    Yamanaka Naoya, Okayama Tomoaki, Oishi Shin'ichi, Ogita Takeshi

    Nonlinear Theory and Its Applications, IEICE   1 ( 1 ) 119 - 132  2010

    　View Summary

    A fast verified automatic integration algorithm is proposed for calculating univariate integrals over finite intervals. This algorithm is based on the double exponential formula proposed by Takahasi and Mori. The double exponential formula uses a certain trapezoidal rule. This trapezoidal rule is determined by fixing two parameters, the width h of a subdivision of a finite interval and the number n of subdivision points of this subdivision. A theorem is presented for calculating h and n as a function of a given tolerance of the verified numerical integration of a definite integral. An efficient a priori method is also proposed for evaluating function calculation errors including rounding errors of floating point calculations. Combining these, a fast algorithm is proposed for verified automatic integration. Numerical examples are presented for illustrating effectiveness of the proposed algorithm.

    DOI CiNii

  • Exact 2D Convex Hull for Floating-point Data

    Katsuhisa Ozaki, Takeshi Ogita, Shin'ichi Oishi

    REC 2010: PROCEEDINGS OF THE 4TH INTERNATIONAL WORKSHOP ON RELIABLE ENGINEERING COMPUTING: ROBUST DESIGN - COPING WITH HAZARDS, RISK AND UNCERTAINTY     282 - 292  2010  [Refereed]

    DOI

  • A Verified Automatic Contour Integration Algorithm

    Naoya Yamanaka, Shin'ichi Oishi, Takeshi Ogita

    REC 2010: PROCEEDINGS OF THE 4TH INTERNATIONAL WORKSHOP ON RELIABLE ENGINEERING COMPUTING: ROBUST DESIGN - COPING WITH HAZARDS, RISK AND UNCERTAINTY     149 - 158  2010  [Refereed]

    DOI

  • Fast Verified Solutions of Linear Systems

    Takeshi Ogita, Shin'ichi Oishi

    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS   26 ( 2-3 ) 169 - 190  2009.10

  • Adaptive and Efficient Algorithm for 2D Orientation Problem

    Katsuhisa Ozaki, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi

    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS   26 ( 2-3 ) 215 - 231  2009.10

    DOI CiNii

    Scopus

    1
    Citation
    (Scopus)

  • Robustness problems and verified computations for computational geometry

    Katsuhisa Ozaki, Takeshi Ogita, Shin'ichi Oishi

    Asia Simulation Conference 2009, JSST 2009    2009

  • Fast and Robust Algorithm for Geometric Predicates using Floating-Point Arithmetic(Practice,Quality of Computation,<Special Issue> "Joint Symposium of JSIAM Activity Groups 2006")

    Ozaki Katsuhisa, Ogita Takeshi, Rump Siegfried M., Oishi Shin'ichi

    Transactions of the Japan Society for Industrial and Applied Mathematics   16 ( 4 ) 553 - 562  2006

    　View Summary

    This paper is concerned with the computational geometry. A number of geometric problems can be boiled down to the determinant predicates, i.e. whether the sign of the determinant is positive, negative or zero. Among such problems, the ORIENT3D is focused in this paper. A fast and adaptive method for rigorously solving ORIENT3D is proposed. The proposed method in this paper is based on a new accurate floating-point summation algorithm which has just been developed by Rump, Ogita and Oishi. The proposed method ideally works with depending on difficulty of the problem, i.e., if the condition number of the problem becomes larger, then the computational cost for the method gradually increases. Numerical results are presented for illustrating that the proposed method is faster than the state-of-the-art method proposed by Demmel-Hida.

    DOI CiNii

  • Numerical Verification Method for Arbitrarily Ill-conditioned Linear Systems(Quality of Computations, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

    Ohta Takahisa, Ogita Takeshi, Rump Siegfried M., Oishi Shinichi

    Transactions of the Japan Society for Industrial and Applied Mathematics   15 ( 3 ) 269 - 286  2005

    　View Summary

    This paper is concerned with the problem of verifying an accuracy of a numerical solution of a linear system with an arbitrarily ill-conditioned coefficient matrix. In this paper, a method of obtaining an accurate numerical solution of such a linear system and its verified error bound is proposed. The proposed method is based on the accurate computation of dot product and IEEE standard 754 arithmetic. A verified and accurate numerical solution with a desired tolerance can be obtained by the proposed method with iterative refinement. Numerical results are presented for illustrating the effectiveness of the proposed method.

    DOI CiNii

  • Numerical Verification for Each Eigenvalues of Symmetric Matrix(Quality of Computations, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

    Miyajima Shinya, Ogita Takeshi, Oishi Shinichi

    Transactions of the Japan Society for Industrial and Applied Mathematics   15 ( 3 ) 253 - 268  2005

    　View Summary

    A fast verification method of calculating guaranteed error bounds for all approximate eigenvalues of a real symmetric matrix is proposed. In the proposed algorithm, Rump's and Wilkinson's bounds are combined. By introducing Wilkinson's bound, it is possible to improve the error bound obtained by the verification algorithm based on Rump's bound with a negligible additional cost. Finally this paper includes some numerical examples to show the efficiency of the proposed method.

    DOI CiNii

  • Fast verification for respective eigenvalues of symmetric matrix

    S Miyajima, T Ogita, S Oishi

    COMPUTER ALGEBRA IN SCIENFIFIC COMPUTING, PROCEEDINGS   3718   306 - 317  2005  [Refereed]

  • Accurate sum and dot product with applications

    Takeshi Ogita, Siegfried M. Rump, ShiN'Ichi Oishi

    Proceedings of the IEEE International Symposium on Computer-Aided Control System Design     152 - 155  2004

▼display all

Books and Other Publications

  • ソフトウェア自動チューニング : 科学技術計算のためのコード最適化技術

    今村, 俊幸, 荻田, 武史, 尾崎, 克久, 片桐, 孝洋, 須田, 礼仁, 高橋, 大介, 滝沢, 寛之, 中島, 研吾

    森北出版  2021.09 ISBN: 9784627872219

  • 固有値計算と特異値計算

    長谷川, 秀彦, 今村, 俊幸, 山田, 進 (計算科学), 櫻井, 鉄也, 荻田, 武史, 相島, 健助, 木村, 欣司, 中村, 佳正, 日本計算工学会

    丸善出版  2019.12 ISBN: 9784621304730

  • 精度保証付き数値計算の基礎

    大石, 進一, 荻田, 武史, 柏木, 雅英, 劉, 雪峰, 尾崎, 克久, 山中, 脩也, 高安, 亮紀, 関根, 晃太, 木村, 拓馬, 市原, 一裕, 正井, 秀俊, 森倉, 悠介, Rump, Siegfried M.

    コロナ社  2018.07 ISBN: 9784339028874

  • マイクロ波シミュレータの基礎

    山下, 栄吉, 電子情報通信学会

    電子情報通信学会  2004.04 ISBN: 4885522013

    ASIN

Research Projects

  • Establishment of Computational Methods for Ultra-Large-Scale Matrix Functions

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2025.04
    -
    2030.03
     

  • 数値線形代数の数値解に対する厳密精度評価の基盤形成

    日本学術振興会  科学研究費助成事業

    Project Year :

    2023.04
    -
    2026.03
     

    尾崎 克久, 荻田 武史, 今村 俊幸

    　View Summary

    今年度は、数値線形代数において重要な連立一次方程式、標準・一般化固有値分解、特異値分解、最小二乗問題に対して研究を推進し、真の特性が事前に既知となるテスト行列生成法を開発した。数値線形代数の問題において、分解フォームのファクタに摂動を加え、複数回の行列積の計算中に丸め誤差が発生しないように設計した。これにより、真の解の目標値をユーザが与えることができ、厳密な解が事前わかる。固有値問題や特異値分解では、重複固有値や特異値の指定も可能である。特に、煩雑な丸め誤差解析を必要としない反復試行的なテスト行列の生成アルゴリズムを開発した。
    数値線形代数では、Cholesky分解、LU分解、QR分解、LDL分解などの代表的な行列分解があり、厳密な分解ファクタがわかるテスト問題の生成アルゴリズムを開発した。さらに高速かつ高精度に精度保証をするフレームワークを開発し，数値実験によって有効性を検証した。
    今後に向けて、高精度計算アルゴリズムを開発した。数値計算の精度が不足する場合には、浮動小数点数の和で数を表現し、その演算を定義したdouble-word, triple-word, quad-word arithmeticという手法がある。本研究では、pair arithmeticの技法を応用して、従来のtriple-wordやquad-wordを高速化した手法を提案した。低コストであり、精度をできるだけ維持するアルゴリズムの工夫も同時に考案した。提案した手法をLU分解やCholesky分解に適用し、疑似正規化という技法を活用することで実用性を示した。
    GPU向けの固有値計算環境で内部における複数精度いわゆる混合精度演算を可能にするための修正を行い、アルゴリズム内部の演算精度の変更、それにともなう計算結果へのインパクト、総合的な計算時間と期待精度との相関を確認するための環境整備を実施した。

  • Fast and accurate eigenvalue calculations by hierarchical low-rank approximation and its application to large-scale electronic structure calculations

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2022.04
    -
    2025.03
     

  • Computer-assisted solution verification for 3D flows with large Reynolds numbers

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2021.04
    -
    2025.03
     

  • 物理学・情報科学に共通する大規模行列関数の総合的数値計算法の創成

    日本学術振興会  科学研究費助成事業

    Project Year :

    2020.04
    -
    2025.03
     

    曽我部 知広, 荻田 武史, 野中 千穂, 宮武 勇登, 田中 健一郎, 星 健夫, 臼田 毅

  • Innovative Methods for Scientific Computing in the Exascale Era by Integrations of (Simulation+Data+Learning)

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2019.06
    -
    2024.03
     

  • 疎行列を係数とする線形方程式の反復解法と精度保証付き数値計算法の融合

    日本学術振興会  科学研究費助成事業

    Project Year :

    2020.04
    -
    2023.03
     

    尾崎 克久, 荻田 武史, 相原 研輔

    　View Summary

    疎行列を係数とする連立一次方程式の精度保証付き数値計算を行うことを目標としている．このためには，係数行列の逆行列の最大値ノルムの上限値が必要であり，これがあれば精度保証は行列サイズの2乗の計算コストで実行可能となる．反復解法に用いる疎行列のデータセットして高名なSuiteSparse Matrix Collectionにある1000以上の行列に対して，逆行列の最大値ノルムの上限を求めることができ，データをweb上に公開した（https://www.mathsci.shibaura-it.ac.jp/ozaki/smc_norminf.html）．これは研究期間全体の目標である行列数の半数を取り扱えたことになる．Rumpによるノルムの精度保証法に加えて高精度計算を適用することにより，ノルムの上限の過大評価を抑えることができ，中には正確な逆行列のノルムや，浮動小数点数として最良な結果を得ることもできた行列もある．これらのデータを活用し，疎行列の精度保証付き数値計算が効率よく実行できること，また残差反復を用いた精度保証付き数値計算は誤差の過大評価を極めて抑え，真の解を包含できることを学会で報告した．特に，近似計算を行う計算時間よりも過大評価のない誤差上限を得るための計算時間が短い例も紹介することができた．また，反復解法における収束性には，行列の固有値が重要であることも知られている．真の固有値を事前に設定することで，反復解法の収束履歴の挙動が正確に把握でき，理論と実践のギャップを調べることができる．よって真の固有値が事前にわかる行列の生成法を開発した．特に，反復解法の解析において重要な複素固有値を持つ実疎行列について，生成法を新しく提案でき，成果を論文として投稿した．以上より，研究初年度は順調に研究を進めることができた．

  • モデリングのための精度保証付き数値計算論の展開

    科学技術振興機構  戦略的な研究開発の推進 戦略的創造研究推進事業 CREST

    Project Year :

    2014
    -
    2021
     

    大石 進一

    　View Summary

    本研究の目的は、計算機による計算の信頼性を保証する精度保証付き数値計算や離散可積分系の数学理論に基づく計算機援用解析手法によって、数理的なモデリングの信頼性や現象との整合性について検討できるような理論を構築し、モデリングに役立つ精度保証付き数値計算学を確立し発展させることです。モデリングに役立つ計算機援用解析という新たな分野を創出し、モデリングの信頼性を飛躍的に向上させることを目指します。

  • Development of accurate algorithms for numerical linear algebra

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2016.04
    -
    2019.03
     

    Ogita Takeshi

    　View Summary

    For linear systems, we conducted on numerical algorithms that can always obtain the best approximate solution regardless of the condition number of the coefficient matrix.
    We developed an iterative improvement algorithm for eigenvectors with quadratic convergence for symmetric eigenvalue problems. This enables us to develop a numerical algorithm that can always obtain the best approximate solution. We also developed a numerical algorithm that can always obtain the best approximate solution of singular value problems for nonsymmetric matrices.
    In order to improve the efficiency of the above proposed algorithms, we developed accurate matrix multiplication algorithms. In addition, as test problems in numerical linear algebra, we developed methods for generating problems with exact solutions.

  • Development of Technologies of High Performance Computing for Accuracy Assurance

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2016.04
    -
    2018.03
     

    KATAGIRI TAKAHIRO, ICHIMURA Syuntaro

    　View Summary

    We establish new implementation methods and performance evaluation for high-precision matrix-matrix multiplication (HP_GEMM). A high-performance thread parallelization method for HP_GEMM is developed by sparselization to reduce computational complexities. In addition, we evaluate several implementation methods with an existing supercomputer. The implementations are utilizing with sparse storage formats, such as CRS and ELL, and dense matrix-matrix multiplication DGEMM, and implementations of sparse matrix-vector multiplications to increase efficiency of threads execution with problem-level parallelisms. Performance of thread execution of the implementations is clarified by the performance evaluation.
    We discuss theory, implementation, and evaluation for accuracy of HP_GEMM. In particular, we develop an algorithm to establish rounding for the immediate floating-point neighbors in error-free transformation of the matrix-matrix computations.

  • Development of robust and efficient algorithms in numerical linear algebra

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2011.04
    -
    2015.03
     

    OGITA Takeshi

    　View Summary

    The purpose of this research is to create a framework of robust matrix factorization algorithms in numerical linear algebra. Since scientific computing is based on numerical linear algebra, development of such algorithms is very important. For this purpose, it was necessary to create a common framework for algorithms rather than considering details of individual algorithms. We succeeded in developing a robust factorization algorithm for real symmetric matrices. Moreover, we proposed robust numerical methods for eigenvalue problems and singular value problems.

  • 非線形系の精度保証付き数値計算法の基盤とエラーフリーな計算工学アルゴリズムの探求

    科学技術振興機構  戦略的な研究開発の推進 戦略的創造研究推進事業 CREST

    Project Year :

    2009
    -
    2014
     

    大石 進一

    　View Summary

    計算機によって数学的に正しい数値計算結果を得るための精度保証付き数値計算学を計算工学の分野へ導入し、それらの諸問題を誤りなく、しかも現実的な計算時間で解けるようにすることが本研究課題の目標です。計算工学に現れる有限次元非線形系に対する精度保証付き数値計算のブレークスルーによって、人が安心して利用できる誤らない計算工学アルゴリズムを設計可能とし、理工学・産業の諸分野に絶大な波及効果をもたらします。

  • Research on fast and accurate verified numerical computations for large-scale systems of linear equations

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2007
    -
    2010
     

    OGITA Takeshi

    　View Summary

    Solving systems of linear equations on computers is ubiquitous in scientific computing. Since numerical computations involve rounding errors, approximate solutions of the systems are obtained. Therefore, it is important to evaluate how accurate the approximate solutions are. In this research, methods of evaluating the accuracy of approximate solutions of large-scale systems of linear equations have been developed with introducing fast and accurate algorithms for calculating dot products, even if the solving problems are ill-conditioned.

  • 数値線形シミュレーションの精度保証に関する研究

    科学技術振興機構  ＪＳＴ戦略的創造研究推進制度（研究チーム型） （戦略的基礎研究推進事業：ＣＲＥＳＴ）

    Project Year :

    2005
    -
    2009
     

    大石 進一

    　View Summary

    本研究では、数値線形シミュレーションツールを精度保証付きシミュレータへと性能向上させる理論とアルゴリズムを確立します。また、高精度内積計算アルゴリズムを用いた、悪条件線形問題の解決アルゴリズムとポータブルな高精度精度保証アルゴリズムを開発します。これらのアルゴリズムは、開発後に既存の有力シミュレータに実装して有効性を確認します。

  • 大規模疎行列系連立一次方程式の数値解の高速な精度保証法に関する研究

    日本学術振興会  科学研究費助成事業

    Project Year :

    2004
    -
    2006
     

    荻田 武史

    　View Summary

    本年度の主な研究成果は以下のとおりである.
    (1)大規模連立一次方程式のための高速精度保証法の開発
    (2)連立一次方程式の数値解に対する非常にシャープな精度保証法の開発
    (3)丸めモードの変更を用いないポータブルな精度保証法の開発
    (4)実対称行列の各固有値・固有ベクトルに対する精度保証付き数値計算法
    (1)に関して,連立一次方程式の精度保証付き数値計算を実用レベルで適用するために,より大規模で広いクラスの疎行列の取り扱いについて考えた.
    その研究成果として,特別な構造を持つクラスの行列のうち,一般化優対角行列,対称正定値行列を係数とするような大規模疎行列系の連立一次方程式に対する高速な精度保証法を考案した.
    (2)に関して,従来の精度保証を拡張し,これまで誤差の上限のみを求めていたものを,下限も同時に求めることにより,精度保証自体の品質を向上させる方式を提案した.
    (3)に関して,JavaやFORTRAN77など言語として丸めモードをサポートしていないような計算環境における連立一次方程式の精度保証付き数値計算について研究した.
    これと高精度内積計算を組み合わせて,丸めモードが利用できない計算環境でも高品質な精度保証が可能となる手法を開発し,それを数値実験で確かめた.
    (4)に関して,実対称行列の各固有値・固有ベクトルに対する精度保証法について研究した.これは,昨年度までに開発してきた固有値の精度保証をさらに発展させたものであり,計算量をほとんど増加させることなく,固有ベクトルに関しても実用的なレベルの誤差限界を得ることができることを示し,さらにそれを数値実験によって確かめた.

▼display all

Misc

  • 尾崎スキームによる無限精度内積と再現可能疎行列反復ソルバーへの応用

    椋木大地, 尾崎克久, 荻田武史, 今村俊幸

    日本応用数理学会年会講演予稿集(CD-ROM)   2022  2022

    J-GLOBAL

  • 不等分割による行列積のエラーフリー変換の高精度計算への応用

    尾崎克久, 椋木大地, 荻田武史, 荻田武史

    日本応用数理学会年会講演予稿集(CD-ROM)   2022  2022

    J-GLOBAL

  • 実対称固有値分解に対する反復改良法の高速化

    内野佑基, 尾崎克久, 荻田武史

    日本応用数理学会年会講演予稿集(CD-ROM)   2021  2022

    J-GLOBAL

  • Acceleration of Error-Free Transformation of Matrix Multiplication using GPU Tensor Cores

    OZAKI Katsuhisa, MUKUNOKI Daichi, OGITA Takeshi

    International Conference on Simulation Technology (CD-ROM)   40th  2021

    J-GLOBAL

  • 実対称行列の固有値分解に対する反復改良法の大規模並列環境における実装と評価

    内野佑基, 尾崎克久, 荻田武史

    情報処理学会研究報告(Web)   2020 ( HPC-177 )  2020

    J-GLOBAL

  • While Paper from Workshop on Large-scale Parallel Numerical Computing Technology (LSPANC 2020): HPC and Computer Arithmetic toward Minimal-Precision Computing

    Roman Iakymchuk, Daichi Mukunoki, Artur Podobas, Fabienne Jézéquel, Toshiyuki Imamura, Norihisa Fujita, Jens Huthmann, Shuhei Kudo, Yiyu Tan, Jens Domke, Kai Torben Ohlhus, Takeshi Fukaya, Takeo Hoshi, Yuki Murakami, Maho Nakata, Takeshi Ogita, Kentaro Sano, Taisuke Boku

    CoRR   abs/2004.04628  2020

  • GPUの単精度演算・Tensorコアを用いた行列積のエラーフリー変換

    尾崎克久, 椋木大地, 荻田武史

    日本応用数理学会年会講演予稿集(CD-ROM)   2020  2020

    J-GLOBAL

  • 尾崎スキームを用いたbinary128による4倍精度行列積

    椋木大地, 尾崎克久, 荻田武史

    日本応用数理学会年会講演予稿集(CD-ROM)   2020  2020

    J-GLOBAL

  • 尾崎スキームによる高精度かつ再現性のあるBLAS実装

    椋木大地, 荻田武史, 尾崎克久, 今村俊幸

    日本応用数理学会年会講演予稿集(CD-ROM)   2019  2019

    J-GLOBAL

  • Level-3BLASに基づく高精度行列積計算法による高精度かつ再現性のあるBLASルーチンの実装とその最適化

    椋木大地, 荻田武史, 尾崎克久

    情報処理学会研究報告(Web)   2018 ( HPC-166 )  2018

    J-GLOBAL

  • A modified algorithm for accurate inverse Cholesky factorization (応用数理と計算科学における理論と応用の融合)

    Yanagisawa Yuka, Ogita Takeshi, Oishi Shin'ichi

    数理解析研究所講究録   ( 2005 ) 56 - 64  2016.11

    CiNii

  • Memory Reduced Implementation of Error-Free Transformation of Matrix Multiplication and Its Performance (The latest developments in theory and application on scientific computation)

    Ozaki Katsuhisa, Ogita Takeshi

    RIMS Kokyuroku   1791   66 - 75  2012.04

    CiNii

  • A Thread Parallelization to Accuracy Guaranteed Matrix-Matrix Multiplication and Implementation of Its Function to ABCLibScript

      2012 ( 26 ) 1 - 8  2012.03

    CiNii

  • 結果の精度を保証するBLASへの依存度が高い行列積アルゴリズムのパフォーマンス

    尾崎克久, 荻田武史

    ハイパフォーマンスコンピューティングと計算科学シンポジウム論文集   2012   64 - 64  2012.01

    CiNii

  • On verified estimation of eigenvalue of generalized matrix eigenvalue problem

      2012   65 - 65  2012.01

    CiNii

  • AN ALGORITHM FOR ACCURATE EIGENVALUE DECOMPOSITION

      15 ( 2 ) 881 - 884  2010.05

    CiNii

  • Iterative Refinement for Ill-Conditioned Linear Systems

    Shin&apos;ichi Oishi, Takeshi Ogita, Siegfried M. Rump

    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS   26 ( 2-3 ) 465 - 476  2009.10

  • A Fast Verified Automatic Integration Algorithm using Double Exponential Formula (Numerical Analysis : Theory, Methods and Applications)

    Yamanaka Naoya, Okayama Tomoaki, Oishi Shin'ichi, Ogita Takeshi

    RIMS Kokyuroku   1638   146 - 158  2009.04

    CiNii

  • Tight Enclosures of Solutions of Linear Systems

    T. Ogita, S. Oishi

    International Series of Numerical Mathematics   157   167 - 178  2009

  • 大規模疎行列の正定値性の保証法 (計算科学の基盤技術としての高速アルゴリズムとその周辺)

    荻田 武史, Rump Siegfried M., 大石 進一

    数理解析研究所講究録   1614   34 - 39  2008.10

    CiNii

  • Robust Geometric Predicates for 3D Orientation Problem by Using Robust Computation of 2D Orientation Problem (High Performance Algorithms for Computational Science and Their Applications)

    OZAKI Katsuhisa, OGITA Takeshi, OISHI Shin'ichi

    RIMS Kokyuroku   1614   1 - 10  2008.10

    CiNii

  • A parallel algorithm for accurate dot product

    N. Yamanaka, T. Ogita, S. M. Rump, S. Oishi

    PARALLEL COMPUTING   34 ( 6-8 ) 392 - 410  2008.07

    DOI

  • 品質を落とさない数値計算法 ー無誤差変換と高精度計算ー

    荻田 武史

    数学セミナー   47 ( 11_566 ) 15 - 19  2008

    CiNii

  • ACCURATE FLOATING-POINT SUMMATION PART II: SIGN, K-FOLD FAITHFUL AND ROUNDING TO NEAREST

    Siegfried M. Rump, Takeshi Ogita, Shin'ichi Oishi

    SIAM JOURNAL ON SCIENTIFIC COMPUTING   31 ( 2 ) 1269 - 1302  2008

    DOI CiNii

  • ACCURATE FLOATING-POINT SUMMATION PART I: FAITHFUL ROUNDING

    Siegfried M. Rump, Takeshi Ogita, Shin'ichi Oishi

    SIAM JOURNAL ON SCIENTIFIC COMPUTING   31 ( 1 ) 189 - 224  2008

    DOI CiNii

  • 行列式の高速な精度保証付き数値計算法(数値シミュレーションを支える応用数理)

    荻田 武史, 尾崎 克久, 大石 進一

    数理解析研究所講究録   1573   45 - 52  2007.11

    CiNii

  • Convergence of Rump's method for inverting arbitrarily ill-conditioned matrices

    Shin'ichi Oishi, Kunio Tanabe, Takeshi Ogita, Siegfried M. Rump

    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS   205 ( 1 ) 533 - 544  2007.08

    DOI

  • Fast Verification of Matrix Determinant

    OGITA Takeshi, OZAKI Katsuhisa, OISHI Shin'ichi

      26   225 - 228  2007.06

    CiNii

  • Fast Verification for Solutions in Least Square Problem

    MIYAJIMA Shinya, OGITA Takeshi, OISHI Shin'ichi

      26   229 - 232  2007.06

    CiNii

  • Fast and Adaptive Algorithm for 2D Orientation Problem

    OZAKI Katsuhisa, OGITA Takeshi, OISHI Shin'ichi

      26   221 - 224  2007.06

    CiNii

  • Super-fast validated solution of linear systems

    Siegfried M. Rump, Takeshi Ogita

    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS   199 ( 2 ) 199 - 206  2007.02

    DOI

  • A method of obtaining verified solutions for linear systems suited for Java

    K. Ozaki, T. Ogita, S. Miyajima, S. Oishi, S. M. Rump

    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS   199 ( 2 ) 337 - 344  2007.02

    DOI

  • 数値シミュレーションを支える精度保証技術

    大石 進一, 荻田 武史

    情報処理   48 ( 10 ) 1103 - 1110  2007

  • Numerical Verification for Each Eigenpair of Symmetric Matrix

    MIYAJIMA Shinya, OGITA Takeshi, OISHI Shin'ichi

      16 ( 4 ) 535 - 552  2006.12

    CiNii

  • Numerical Verification Method for Systems of Linear Equations Using Accurate Computation of Dot Product(<Special Issue> Robust Computation and Its Verification)

    Oishi Shin'ichi, Ogita Takeshi, Ohta Takahisa

    Journal of the Japan Society for Simulation Technology   25 ( 3 ) 170 - 178  2006.09

    　View Summary

    IEEE standard 754 is widely used as a standard of floating-point arithmetic. Most of CPUs in today's computers support IEEE standard 754. Using double precision arithmetic following IEEE standard 754, the authors have proposed fast methods of verifying the accuracy of a numerical solution of a linear system. In this paper, an accurate and fast verification method for a linear system is developed using residual iteration method. The residual iteration requires the availability of high precision computation. Up to now, extended precision, i.e. multiple precision and quadruple precision are used for the accurate computation of the residual. However, such higher precision arithmetic systems are not necessarily available on all computers. Therefore, the residual iteration using such systems does not have the portability. In this paper, an accurate, fast and portable method for a linear system using the fact that an algorithm of accurate dot product can portably be implemented and applied to the residual iteration. Finally, numerical results are presented showing the effectiveness of the proposed verification method.

    CiNii

  • Memory Reduced Verification Method for Systems of Linear Equations(<Special Issue> Robust Computation and Its Verification)

    Ogita Takeshi, Oishi Shin'ichi

    Journal of the Japan Society for Simulation Technology   25 ( 3 ) 179 - 184  2006.09

    　View Summary

    In this paper, new verification methods for verifying the accuracy of a numerical solution of a linear system with a dense coefficient matrix are proposed. The proposed methods are based on a verification method which uses an approximate inverse of the coefficient matrix. It is possible to reduce the computational memory space for the verification drastically without slowing down its computational speed seriously. Numerical results are presented to illustrate that the proposed methods become more effective in larger problem size.

    CiNii

  • Verified Solutions of Extremely Ill-conditioned Linear Systems

    OHTA Takahisa, OGITA Takeshi, RUMP Siegfried M., OISHI Shin'ichi

      24   225 - 228  2005.07

    CiNii

  • Accurate, Verified and Portable Standard Functions and its Applications

    OZAKI Katsuhisa, OGITA Takeshi, OISHI Shin'ichi

      24   193 - 196  2005.07

    CiNii

  • Verification for Each Eigenvalues of Symmetric Matrix

    MIYAJIMA Shinya, OGITA Takeshi, OISHI Shin'ichi

      24   229 - 232  2005.07

    CiNii

  • Numerical Verification Method for Systems of Linear Equations in Java (New Development of Numerical Analysis in the 21st Century)

    Ozaki Katsuhisa, Ogita Takeshi, Miyajima Shinya, Oishi Shin'ichi

    RIMS Kokyuroku   1441   75 - 88  2005.07

    CiNii

  • Fast Verification Method for Large-scale Linear Systems

    OGITA TAKESHI, OISHI SHIN'ICHI

      46 ( 10 ) 10 - 18  2005.06

    　View Summary

    This paper is concerned with the problem of verifying the accuracy of the approximate solutions of large-scale dense linear systems. In this paper, the guaranteed error bounds on computed solutions of large-scale linear systems are calculated. Results of numerical experiments have elucidated the limit of applicability of the previous verification methods for large-scale problems under certain conditions. To overcome this, a new verification method is proposed for large-scale problems. Finally, the performance of the proposed method is evaluated.

    CiNii

  • Fast inclusion of interval matrix multiplication

    Takeshi Ogita, Shin'ichi Oishi

    Reliable Computing   11 ( 3 ) 191 - 205  2005.06

    DOI

  • Accurate sum and dot product

    T Ogita, SM Rump, S Oishi

    SIAM JOURNAL ON SCIENTIFIC COMPUTING   26 ( 6 ) 1955 - 1988  2005

    DOI

  • Numerical Inclusion Method for All Eigenvalues of Real Symmetric Definite Generalized Eigenvalue Problem

    MARUYAMA Kosuke, OGITA Takeshi, NAKAYA Yusuke, OISHI Shin'ichi

    The Transactions of the Institute of Electronics, Information and Communication Engineers A   87 ( 8 ) 1111 - 1119  2004.08

    CiNii

  • Verification of Nonsingularity for Sparse Matrices using Direct Solution Methods

    OGITA Takeshi, OISHI Shin'ichi

      23   349 - 352  2004.06

    CiNii

  • Numerical Verification Method for Simultaneous Linear Equations using Accurate Dot Product Calculation Algorithm

    OHTA Takahisa, OISHI Shin'ichi, OGITA Takeshi, RUMP Siegfried M.

      23   345 - 348  2004.06

    CiNii

  • Fast Verification for Systems of Linear Equations with the Extended Strassen's Method (Numerical Analysis and New Information Technology)

    Moriyama Atsushi, Ogita Takeshi, Ushiro Yasunori, Oishi Shin'ichi

    RIMS Kokyuroku   1362   47 - 55  2004.04

    CiNii

  • 計算機援用証明II

    S. M. Rum

    応用数理   14 ( 4 ) 44 - 57  2004

  • Computer-Assisted Proof I

    Rump Siegfried M., Ogita (translation) Takeshi

    Bulletin of the Japan Society for Industrial and Applied Mathematics   14 ( 3 ) 214 - 223  2004

    　View Summary

    We will discuss the possibility to 'prove' mathematical theorems with the aid of digital computers and present different methods to approach this goal. Special focus will be on integer and floating point arithmetic, on computer algebra methods as well as on so-called selfvalidating methods. This note can only cover a very small part of the subject and is intended to stimulate discussions, and possibly reconsideration of one or the other point of view.

    DOI CiNii

  • Computation of sharp rigorous componentwise error bounds for the approximate solutions of systems of linear equations

    Takeshi Ogita, Shin'ichi Oishi, Yasunori Ushiro

    Reliable Computing   9 ( 3 ) 229 - 239  2003.06

    DOI

  • Strassen のアルゴリズムによる行列乗算の高速精度保証 (微分方程式の数値解法と線形計算)

    荻田 武史, 大石 進一, 後 保範

    数理解析研究所講究録   1320   151 - 161  2003.05

    CiNii

  • Fast Inclusion and Residual Iteration for Solutions of Matrix Equations

    T. Ogita, S. Oishi, Y. Ushiro

    Computing   Supplement ( 16 ) 171 - 184  2002

  • Fast Verification of Numerical Solutions of Matrix Equations by Iterative Solution Methods

    OGITA Takeshi, OISHI Shin'ichi, USHIRO Yasunori

      20   249 - 252  2001.06

    CiNii

  • 単調な疎行列における連立一次方程式の高速精度保証 (偏微分方程式の数値解法とその周辺II)

    荻田 武史, 後 保範, 大石 進一

    数理解析研究所講究録   1198   161 - 169  2001.04

    CiNii

  • Fast Verification of Solutions for Sparse Monotone Matrix Equations

    T. Ogita, S. Oishi, Y. Ushiro

    Computing   Supplement ( 15 ) 175 - 187  2001

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Syllabus

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Sub-affiliation

  • Faculty of Science and Engineering   Graduate School of Fundamental Science and Engineering

Research Institute

  • 2024
    -
    2026

    Waseda Research Institute for Science and Engineering   Concurrent Researcher

Internal Special Research Projects

  • 科学技術計算における品質管理及び信頼性向上のための精度保証付き数値計算

    2002  

    　View Summary

    本年度は、対称行列における連立一次方程式の数値解の精度保証、その保証精度の高精度化、そして分散型並列計算機（PCクラスタ）上での連立一次方程式の数値解の精度保証および行列の固有値の精度保証に関する研究、さらに、内積計算の高精度計算に関する研究を行った。2002年度の研究発表は以下の通りである。1. 荻田 武史, 後 保範, 大石 進一: スパース行列用直接解法の高速化と精度保証, 第31回数値解析シンポジウム(NAS2002) 講演予稿集, pp.33-36 (2002/6/12-14) 2. 荻田 武史, 西蔭 崇一, 大石 進一: 大規模行列に対する連立一次方程式の数値解の精度保証, 日本応用数理学会 2002年度年会 (2002/9/19-21) 3. 荻田 武史: （依頼セミナー）連立一次方程式の数値解に対する精度保証の現状, LA研究会, 東京大学理学部 (2002/11/16) 4. 荻田 武史: （依頼セミナー）連立一次方程式の数値解の精度保証と並列計算, 第56回 関西可積分系セミナー, 京都大学工学部 (2002/11/19) 5. 荻田 武史, 大石 進一, 後 保範: （依頼講演）Strassenのアルゴリズムによる行列乗算の高速精度保証, 研究集会 [微分方程式の数値解法と線形計算], 京大数理解析研究所 (2002/11/20-22) 1では，係数行列がスパース行列（非ゼロ要素が極めて少ない行列）である場合に，直接解法によって高速に数値解を得る方法とその精度保証をする方法を提案した。2では，PCクラスタを用いて精度保証をするときの問題点と解決案を示した。3では，連立一次方程式に対する精度保証方法の現状についてまとめ，今後の課題を示した。4では，連立一次方程式に対する精度保証方法とPCクラスタへの適用例を示した。5では，線形計算の基本である行列乗算の高速な数値計算法に精度保証付き数値計算を適用する新しい方法を提案した。

  • 科学技術計算における品質管理と信頼性向上のための精度保証付き数値計算

    2001  

    　View Summary

    本年度は，係数行列がそれぞれ単調行列・対称行列・正定値行列であるような連立一次方程式の数値解の精度保証，その保証精度の高精度化，そして分散型並列計算機（PC cluster）上での連立一次方程式の数値解の精度保証に関する研究を行った。その研究成果の発表（講演）は以下のようである。1. 単調な疎行列における連立一次方程式の数値解の高精度保証, 第30回数値解析シンポジウム(NAS2001) (2001/5/23-25) 2. 反復解法による連立一次方程式の数値解の高速精度保証, 日本シミュレーション学会大会 (2001/6/20-21) 3. Fast inclusion and residual iteration for solutions of matrix equations, International Conference on RECENT ADVANCES IN COMPUTATIONAL MATHEMATICS (ICRACM2001) (October 10-13 2001)4. PCクラスタ上での連立一次方程式の解の精度保証（パネラー）, 電子情報通信学会ソサイエティ大会 (2001/9/18-21)5. Fast verification of solutions for symmetric matrix equations, The International Conference on Fundamental of Electronics Communication and Computer Sciences (March 27-28 2002)1では，係数行列が単調行列である場合を例にして，提案する精度保証法が数値解の本来持っている精度を高速かつほぼ正確に保証できることを示した。2では，係数行列が疎行列のとき，その連立一次方程式は反復解法で解くことが多いが，そのような場合でも行列が特殊な構造を持っているときは精度保証も可能であることを示した。3では，1をさらに発展させ，精度保証と残差反復を組み合わせた新しい方法を示した。4では，これまでの研究成果が分散型並列計算機上にも適用可能であるが，しかし，計算の大規模化によって新たな問題点が生まれることも示した。5では，係数行列が対称行列あるいは正定値対称行列であるような連立一次方程式の数値解の精度保証法を提案した。これは，特に現実的な物理モデルの問題に対して有効である。