List of publications by T. Ogita

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[学術論文 (Journal Paper)]

（投稿中） （英文誌 (International Journal)）
  1. K. Ozaki, D. Mukunoki, T. Ogita: Extension of accurate numerical algorithms for matrix multiplication based on error-free transformation, Japan Journal of Industrial and Applied Mathematics, accepted for publication.
  2. S. M. Rump, T. Ogita: Verified error bounds for matrix decompositions, SIAM Journal on Matrix Analysis and Applications, accepted for publication.
  3. S. M. Rump, T. Ogita: On a quality measure for interval inclusions, BIT Numerical Mathematics, 64 (2024), Article Number 22. [DOI: https://doi.org/10.1007/s10543-024-01020-1]
  4. K. Ozaki, T. Ogita: Generation of test matrices with specified eigenvalues using floating-point arithmetic, Numerical Algorithms, 90 (2022), 241-262. [DOI: https://doi.org/10.1007/s11075-021-01186-7]
  5. K. Ozaki, T. Terao, T. Ogita, T. Katagiri: Verified numerical computations for large-scale linear systems, Applications of Mathematics, 66:2 (2021), 269-285. [DOI: https://doi.org/10.21136/AM.2021.0318-19]
  6. K. Ozaki, T. Ogita: The essentials of verified numerical computations, rounding error analyses, interval arithmetic, and error-free transformations, Nonlinear Theory and Its Applications, IEICE, Vol. 11, No. 3 (2020), 279-302. [DOI: https://doi.org/10.1587/nolta.11.279]
  7. T. Hoshi, T. Ogita, K. Ozaki, T. Terao: An a posteriori verification method for generalized real-symmetric eigenvalue problems in large-scale electronic state calculations, Journal of Computational and Applied Mathematics, 376 (2020), Article 112830. [DOI: 10.1016/j.cam.2020.112830]
  8. D. Mukunoki, T. Ogita: Performance and energy consumption of accurate and mixed-precision linear algebra kernels on GPUs, Journal of Computational and Applied Mathematics, 372 (2020), Article 112701. [DOI: 10.1016/j.cam.2019.112701]
  9. A. Minamihata, T. Ogita, S. M. Rump, S. Oishi: Modified error bounds for approximate solutions of dense linear systems, Journal of Computational and Applied Mathematics, 369 (2020), Article 112546. [DOI: 10.1016/j.cam.2019.112546]
  10. T. Terao, K. Ozaki, T. Ogita: LU-Cholesky QR algorithms for thin QR decomposition, Parallel Computing, 92 (2020), Article 102571. [DOI: https://doi.org/10.1016/j.parco.2019.102571]
  11. D. Mukunoki, T. Ogita, K. Ozaki: Reproducible BLAS routines with tunable accuracy using Ozaki scheme for many-core architectures, Lecture Notes in Computer Science, 12043 (2020), 516-527. [DOI: https://doi.org/10.1007/978-3-030-43229-4] (Proceedings of the 13th International Conference, PPAM 2019, Bialystok, Poland, September 8–11, 2019, Revised Selected Papers, Part I)
  12. T. Ogita, K. Aishima: Iterative refinement for singular value decomposition based on matrix multiplication, Journal of Computational and Applied Mathematics, 369 (2020), Article 112512. [DOI: 10.1016/j.cam.2019.112512]
  13. T. Ogita, K. Aishima: Iterative refinement for symmetric eigenvalue decomposition II: clustered eigenvalues, Japan Journal of Industrial and Applied Mathematics, Vol. 36, Issue 2 (2019), pp. 435-459. [DOI: 10.1007/s13160-019-00348-4]
  14. T. Ogita, K. Aishima: Iterative refinement for symmetric eigenvalue decomposition, Japan Journal of Industrial and Applied Mathematics, Vol. 35, Issue 3 (2018), pp.1007-1035. [DOI: 10.1007/s13160-018-0310-3]
  15. K. Ozaki, T. Ogita: Generation of linear systems with specified solutions for numerical experiments, Reliable Computing, Vol. 25 (2017), pp.148-167. (Special volume containing refereed papers from SCAN 2016)
  16. Y. Kobayashi, T. Ogita, K. Ozaki: Acceleration of a preconditioning method for ill-conditioned dense linear systems by use of a BLAS-based method, Reliable Computing, Vol. 25 (2017), pp.15-23. (Special volume containing refereed papers from SCAN 2016)
  17. K. Ozaki, T. Ogita, S. Oishi: Error-free transformation of matrix multiplication with a posteriori validation, Numerical Linear Algebra with Applications, Vol. 23, Issue 5 (2016), pp.931-946. [DOI: 10.1002/nla.2061]
  18. S. M. Rump, T. Ogita, Y. Morikura, S. Oishi: Interval arithmetic with fixed rounding mode, Nonlinear Theory and Its Applications, IEICE, Vol. 7, No. 3 (2016), 362-373. [DOI: 10.1587/nolta.7.362]
  19. Y. Kobayashi, T. Ogita: Accurate and efficient algorithm for solving ill-conditioned linear systems by preconditioning methods, Nonlinear Theory and Its Applications, IEICE, Vol. 7, No. 3 (2016), 374-385. [DOI: 10.1587/nolta.7.374]
  20. K. Ozaki, F. Bünger, T. Ogita, S. Oishi, S. M. Rump: Simple floating-point filters for the two-dimensional orientation problem, BIT Numerical Mathematics, Vol. 56, Issue 2 (2016), 729-749. [DOI: 10.1007/s10543-015-0574-9]
  21. K. Ozaki, T. Ogita, S. Oishi: Improvement of error-free splitting for accurate matrix multiplication, Journal of Computational and Applied Mathematics, 288 (2015), 127-140. [DOI: 10.1016/j.cam.2015.04.010]
  22. K. Ozaki, T. Ogita, F. Bünger, S. Oishi: Accelerating interval matrix multiplication by mixed precision arithmetic, Nonlinear Theory and Its Applications, IEICE, 6:3 (2015), 364-376. [DOI: 10.1587/nolta.6.364]
  23. A. Minamihata, K. Sekine, T. Ogita, S. M. Rump, S. Oishi: Improved error bounds for linear systems with H-matrices, Nonlinear Theory and Its Applications, IEICE, 6:3 (2015), 377-382. [DOI: 10.1587/nolta.6.377]
  24. K. Kobayashi, T. Ogita: Backward error bounds for 2 x 2 linear systems arising in the diagonal pivoting method, Nonlinear Theory and Its Applications, IEICE, 6:3 (2015), 383-390. [DOI: 10.1587/nolta.6.383]
  25. Y. Kobayashi, T. Ogita: A fast and efficient algorithm for solving ill-conditioned linear systems, JSIAM Letters, 7 (2015), 1-4.
  26. A. Minamihata, K. Sekine, T. Ogita, S. Oishi: Fast verified solutions of sparse linear systems with H-matrices, Reliable Computing, 19:2 (2013), 127-141. (Special volume devoted to material presented at SCAN 2012)
  27. K. Ozaki, T. Ogita, S. Oishi, S. M. Rump: Generalization of error-free transformation for matrix multiplication and its application, Nonlinear Theory and Its Applications, IEICE, 4:1 (2013), 2-11.
  28. K. Ozaki, T. Ogita, S. Oishi: A robust algorithm for geometric predicate by error-free determinant transformation, Information and Computation, 216 (2012), 3-13.
  29. K. Ozaki, T. Ogita, S. M. Rump, S. Oishi: Fast algorithms for floating-point interval matrix multiplication, Journal of Computational and Applied Mathematics, 236:7 (2012), 1795-1814.
  30. J. Sengoku, M. Naito, H. Okamoto, T. Ogita, S. Ichikawa: On the visibility of fast reactions in electrochemical impedance spectroscopy, Chemical Physics Letters, 525-526 (2012), 125-128.
  31. T. Ogita, S. Oishi: Accurate and robust inverse Cholesky factorization, Nonlinear Theory and Its Applications, IEICE, 3:1 (2012), 103-111. [PDF]
  32. T. Ogita: Accurate and verified numerical computation of the matrix determinant, International Journal of Reliability and Safety, 6:1-3 (2012), 242-254. (Special Issue based on REC2010) [PDF]
  33. K. Ozaki, T. Ogita, S. Oishi, S. M. Rump: Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications, Numerical Algorithms, 59:1 (2012), 95-118.
  34. N. Yamanaka, M. Kashiwagi, S. Oishi, T. Ogita: A note on a verified automatic integration algorithm, Reliable Computing, 15:2 (2011), 156-167. (Special volume devoted to material presented at SCAN 2008)
  35. K. Ozaki, T. Ogita, S. Oishi: An algorithm for automatically selecting a suitable verification method for linear systems, Numerical Algorithms, 56:3 (2011), 363-382.
  36. K. Ozaki, T. Ogita, S. Oishi: Tight and efficient enclosure of matrix multiplication by using optimized BLAS, Numerical Linear Algebra with Applications, 18:2 (2011), 237-248. (Special Issue on Matrix Computation and Nonlinear Equations)
  37. N. Yamanaka, T. Okayama, S. Oishi, T. Ogita: A fast verified automatic integration algorithm using double exponential formula, Nonlinear Theory and Its Applications, IEICE, 1:1 (2010), 119-132.
  38. S. M. Rump, T. Ogita, S. Oishi: Fast high precision summation, Nonlinear Theory and Its Applications, IEICE, 1:1 (2010), 2-24. [PDF]
  39. T. Ogita: Accurate matrix factorization: Inverse LU and inverse QR factorizations, SIAM Journal on Matrix Analysis and Applications, 31:5 (2010), 2477-2497. [PDF]
  40. S. Miyajima, T. Ogita, S. M. Rump, S. Oishi: Fast verification for all eigenpairs in symmetric positive definite generalized eigenvalue problem, Reliable Computing, 14 (2010), 24-45.
  41. T. Ogita, S. Oishi: Fast verified solutions of linear systems, Japan Journal of Industrial and Applied Mathematics, 26:2-3 (2009), 169-190. (Special Issue on State of the Art in Self-validating Numerical Computations) [PDF]
  42. K. Ozaki, T. Ogita, S. M. Rump, S. Oishi: Adaptive and efficient algorithm for 2D orientation problem, Japan Journal of Industrial and Applied Mathematics, 26:2-3 (2009), 215-231. (Special Issue on State of the Art in Self-validating Numerical Computations)
  43. S. Oishi, T. Ogita, S. M. Rump: Iterative refinement for ill-conditioned linear systems, Japan Journal of Industrial and Applied Mathematics, 26:2-3 (2009), 465-476. (Special Issue on State of the Art in Self-validating Numerical Computations)
  44. T. Ogita, S. Oishi: Tight enclosures of solutions of linear systems, International Series of Numerical Mathematics, 157 (2009), 167-178. (Inequalities and Applications, C. Bandle, A. Gilányi, L. Losonczi, Z. Páles, M. Plum eds., Birkhäuser Verlag) [PDF]
  45. S. M. Rump, T. Ogita, S. Oishi: Accurate floating-point summation part II: Sign, K-fold faithful and rounding to nearest, SIAM Journal on Scientific Computing, 31:2 (2008), 1269-1302. [PDF]
  46. S. M. Rump, T. Ogita, S. Oishi: Accurate floating-point summation part I: Faithful rounding, SIAM Journal on Scientific Computing, 31:1 (2008), 189-224. [PDF]
  47. N. Yamanaka, T. Ogita, S. M. Rump, S. Oishi: A parallel algorithm for accurate dot product, Parallel Computing, 34:6-8 (2008), 392-410. [PDF]
  48. S. Oishi, K. Tanabe, T. Ogita, S. M. Rump: Convergence of Rump's method for inverting arbitrarily ill-conditioned matrices, Journal of Computational and Applied Mathematics, 205:1 (2007), 533-544. [PDF]
  49. S. M. Rump, T. Ogita: Super-fast validated solution of linear systems, Journal of Computational and Applied Mathematics, 199:2 (2007), 199-206. (Special Issue on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2004)) [PDF]
  50. K. Ozaki, T. Ogita, S. Miyajima, S. Oishi, S. M. Rump: A method of obtaining verified solutions for linear systems suited for Java, Journal of Computational and Applied Mathematics, 199:2 (2007), 337-344. (Special Issue on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2004)) [PDF]
  51. T. Ogita, S. M. Rump, S. Oishi: Accurate sum and dot product, SIAM Journal on Scientific Computing, 26:6 (2005), 1955-1988. [PDF]
  52. T. Ogita, S. Oishi: Fast inclusion of interval matrix multiplication, Reliable Computing, 11:3 (2005), 191-205. [PDF]
  53. S. Miyajima, T. Ogita, S. Oishi: Fast verification for respective eigenvalues of symmetric matrix, Lecture Notes in Computer Science, 3718 (2005), 306-317. (Proceedings of the 8th International Workshop on Computer Algebra in Scientific Computing, V. G. Ganzha, E. W. Mayr, E. V. Vorozhtsov eds., Springer-Verlag, Berlin/Heidelberg)
  54. T. Ogita, S. Oishi, Y. Ushiro: Computation of sharp rigorous componentwise error bounds for the approximate solutions of systems of linear equations, Reliable Computing, 9:3 (2003), 229-239. [PDF]
  55. T. Ogita, S. Oishi, Y. Ushiro: Fast inclusion and residual iteration for solutions of matrix equations, Computing, Supplement 16 (2002), 171-184. (Inclusion Methods for Nonlinear Problems: With Applications in Engineering, Economics and Physics, J. Herzberger ed., Springer WienNewYork, Austria) [PDF]
  56. T. Ogita, S. Oishi, Y. Ushiro: Fast verification of solutions for sparse monotone matrix equations, Computing, Supplement 15 (2001), 175-187. (Topics in Numerical Analysis: With Special Emphasis on Nonlinear Problems, G. Alefeld and X. Chen eds., Springer WienNewYork, Austria) [PDF]
（和文誌 (Domestic Journal)）
  1. 内野 佑基, 尾崎 克久, 荻田 武史: 実対称固有値分解に対する反復改良法の高速化, 情報処理学会論文誌：コンピューティングシステム, 15:1 (2022), 1-12.
  2. 宮島 信也, 荻田 武史, 大石 進一: 実対称行列の各固有対の精度保証付き数値計算法, 日本応用数理学会論文誌, 16:4 (2006), 535-552.
  3. 尾崎 克久, 荻田 武史, S. M. Rump, 大石 進一: 点と平面との位置関係を判定する高速かつロバストなアルゴリズム, 日本応用数理学会論文誌, 16:4 (2006), 553-562.
  4. 大石 進一, 荻田 武史, 太田 貴久: 高精度内積計算アルゴリズムを用いた連立一次方程式の精度保証付き数値計算法, シミュレーション, 25:5 (2006), 170-178. (論文特集：ロバスト計算と精度保証)
  5. 荻田 武史, 大石 進一: 連立一次方程式のメモリ量を低減した精度保証付き数値計算法, シミュレーション, 25:5 (2006), 179-184. (論文特集：ロバスト計算と精度保証)
  6. 宮島 信也, 荻田 武史, 大石 進一: 実対称行列の各固有値に対する精度保証付き数値計算法, 日本応用数理学会論文誌, 15:3 (2005), 253-268.
  7. 太田 貴久, 荻田 武史, S. M. Rump, 大石 進一: 悪条件連立一次方程式の精度保証付き数値計算法, 日本応用数理学会論文誌, 15:3 (2005), 269-287.
  8. 荻田 武史, 大石 進一: 大規模連立一次方程式のための高速精度保証法, 情報処理学会論文誌：数理モデル化と応用, 46:SIG10 (TOM12) (2005), 10-18.
  9. 丸山 晃佐, 荻田 武史, 中谷 祐介, 大石 進一: 実対称定値一般化固有値問題のすべての固有値の精度保証付き数値計算法, 電子情報通信学会論文誌, J87-A:8 (2004), 1111-1119.


[解説記事等 (Survey)]

  1. 荻田 武史: スパース系線形方程式の精度保証付き数値計算, 数学セミナー, 612 (2012年10月号), 日本評論社, 26-31. （特集: 計算の性能—速度・環境・正確さ）
  2. 荻田 武史: 連立一次方程式の解に対する精度保証付き数値計算, シミュレーション, 31:3 (2012), 139-143. [PDF]
  3. 尾崎克久, 荻田武史, 大石進一: 有向丸めの変更を使用しないタイトな行列積の包含方法, 応用数理, 21:3 (2011), 22-32.
  4. 荻田 武史: エラーフリー変換がもたらす数値計算の新たな方向性, 数理科学, 578 (2011年8月号), 52-53. [PDF]
  5. 大石 進一, 荻田 武史: 精度保証付シミュレーション技術研究委員会, シミュレーション, 30:1 (2011). [PDF]
  6. 荻田 武史: 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, 数学セミナー, 566 (2008年11月号), 日本評論社, 15-19. （特集: 計算の品質─精度・誤差・効率）[PDF]
  7. 大石 進一, 荻田 武史: 数値シミュレーションを支える精度保証技術, 情報処理, 48:10 (2007), 1103-1110. [PDF]
  8. 荻田 武史, 大石 進一: 精度保証付き数値計算とシミュレーション, 分子シミュレーション研究会会誌「アンサンブル」, 9:2 (2007), 11-16. [PDF]
  9. Siegfried M. Rump （荻田 武史訳）: 計算機援用証明 II, 応用数理, 14:4 (2004), 44-57. [PDF]
  10. Siegfried M. Rump （荻田 武史訳）: 計算機援用証明 I, 応用数理, 14:3 (2004), 214-223. [PDF]


[著書 (Book)]

  1. 分担: ソフトウェア自動チューニング（ISBN: 978-4-627-87221-9）, 森北出版, 2021年9月.（担当: 5章「これからの数値計算：計算結果の保証」pp.261-289）
  2. 分担: 固有値計算と特異値計算（日本計算工学会 編, ISBN: 978-4-621-30473-0）, 丸善出版, 2019年12月.（担当: 5章「反復改良法」pp.127-139）
  3. 分担: 精度保証付き数値計算の基礎（大石進一 編, ISBN: 978-4-339-02887-4）, コロナ社, 2018年7月26日.（担当: 序章 pp.1-10, 1章 pp.11-32, 2章 pp.33-55, 3章 pp.56-90, 9.5節 pp.290-305（和訳））
  4. 分担: 朝倉 数学辞典（川又雄二郎 ・坪井俊 ・楠岡成雄 ・新井仁之 編, ISBN: 978-4-254-11125-5）, 朝倉書店, 2016年6月6日.（担当: 近似計算, pp.150-151, 数値積分, pp.273-274, 補間公式, pp.575-576）
  5. 分担: 応用数理ハンドブック（日本応用数理学会 監修／薩摩順吉 ・大石進一 ・杉原正顕 編, ISBN: 978-4-254-11141-5）, 朝倉書店, 2013年11月15日.（担当: 連立一次方程式に対する精度保証, pp.430-433, 行列固有値問題に対する精度保証, pp.434-437）
  6. 分担: シミュレーション辞典（日本シミュレーション学会編, ISBN: 978-4-339-02458-6）, コロナ社, 2012.（担当: 数値計算と浮動小数点数, p.161, ベクトルと行列のノルム, p.306）
  7. 分担: マイクロ波シミュレータの基礎 (山下榮吉監修, ISBN: 4-88552-201-3), 電子情報通信学会, 2004.（8章: 大規模行列の扱い方, pp.147-167）


[編集 (Editorial Work)]

  1. M. T. Nakao, T. Ogita, S. M. Rump: 18th International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations (SCAN 2018), dedicated to Professor Shin’ichi Oishi on the occasion of his 65th birthday, Journal of Computational and Applied Mathematics, 382 (2021) 113078.
  2. D. Takahashi, T. Ogita: Special Section on Rigorous Nonlinear Analysis, Nonlinear Theory and Its Applications, IEICE, 7:3 (2016), 312.
  3. T. Ogita, K. Ozaki, S. M. Rump: Special Section on Recent Progress in Verified Numerical Computations, Nonlinear Theory and Its Applications, IEICE, 6:3 (2015), 340.
  4. N. Yamamoto, T. Ogita: Special Section on Recent Progress in Verified Numerical Computations, Nonlinear Theory and Its Applications, IEICE, 5:1 (2014), 1.
  5. Z. Arai, T. Ogita, Y. Watanabe: Special Section on Recent Progress in Verified Numerical Computations, Nonlinear Theory and Its Applications, IEICE, 4:1 (2013), 1.


[国際会議論文 (International Conference Paper)]

  1. K. Nakajima, T. Ogita, M. Kawai: Efficient Parallel Multigrid Methods on Manycore Clusters with Double/Single Precision Computing, Proceedings of the 2021 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW), 2021, pp.760-769.
  2. T. Terao, K. Ozaki, T. Ogita: Verified Numerical Computations for Standard Eigenvalue Problems on Supercomputers, Proceedings of the 38th JSST Annual International Conference on Simulation Technology (JSST2019), Miyazaki, Japan, 2019, pp.12-15.
  3. K. Ozaki, T. Ogita, S. Oishi: Matrix Multiplication with Guaranteed Accuracy by Level 3 BLAS, AIP Conference Proceedings, 1504 (2012), 1128-1133.
  4. T. Ogita: Robust Computation of Determinant, AIP Conference Proceedings, 1504 (2012), 1119-1123.
  5. T. Ogita: Accurate Matrix Singular Values, Proceedings of 2010 International Symposium on Nonlinear Theory and its Applications (NOLTA2010), Krakow, Poland, 2010, 140-143.
  6. K. Ozaki, T. Ogita, S. Oishi: Condition Numbers of Two-Dimensional Orientation Problem, Proceedings of 2010 International Symposium on Nonlinear Theory and its Applications (NOLTA2010), Krakow, Poland, 2010, 144-148.
  7. T. Ogita, S. Oishi: Accurate and Robust Inverse Cholesky Factorization, Proceedings of 2009 International Symposium on Nonlinear Theory and its Applications, Sapporo, Japan, 2009, 155-158.
  8. S. Oishi, T. Ogita, S. M. Rump: Iterative Refinement for Ill-Conditioned Linear Equations, Proceedings of 2008 International Symposium on Nonlinear Theory and its Applications, Budapest, Republic of Hungary, 2008, 516-519.
  9. K. Ozaki, T. Ogita, S. M. Rump, S. Oishi: Accurate Matrix Multiplication by Using Level 3 BLAS Operation, Proceedings of 2008 International Symposium on Nonlinear Theory and its Applications, Budapest, Republic of Hungary, 2008, 508-511.
  10. N. Yamanaka, T. Ogita, M. Kashiwagi, S. Oishi: Fast Verified Automatic Integration Algorithm Using Complex Analysis, Proceedings of 2008 International Symposium on Nonlinear Theory and its Applications, Budapest, Republic of Hungary, 2008, 512-515.
  11. T. Nishi, T. Ogita, S. Oishi, S. M. Rump: A Method for the Generation of a Class of Ill-Conditioned Matrices, Proceedings of 2008 International Symposium on Nonlinear Theory and its Applications, Budapest, Republic of Hungary, 2008, 53-56.
  12. T. Nishi, Y. Nakaya, T. Ogita, S. Oishi: A Class of Ill-conditioned Nonlinear Algebraic Equations, Proceedings of 2007 International Symposium on Nonlinear Theory and its Applications, Vancouver, Canada, 2007, 172-175.
  13. T. Ogita, S. Oishi: Tight Error Bounds for Approximate Solutions of Linear Systems, Proceedings of 2007 International Symposium on Nonlinear Theory and its Applications, Vancouver, Canada, 2007, 345-348.
  14. K. Ozaki, T. Ogita, S. M. Rump, S. Oishi: Accurate Matrix Multiplication with Multiple Floating-point Numbers, Proceedings of 2007 International Symposium on Nonlinear Theory and its Applications, Vancouver, Canada, 2007, 337-340.
  15. T. Ogita, S. Oishi: Tight Enclosures of Solutions of Linear Systems, Proceedings of International Conference of Numerical Analysis and Applied Mathematics 2006, Crete, Greece, Wiley-VCH Verlag, 516-519.
  16. S. Oishi, T. Ogita, S. M. Rump: Numerical verification for solutions of finite dimensional sparse linear equations using iterative methods, Proceedings of International Conference of Numerical Analysis and Applied Mathematics 2006, Crete, Greece, Wiley-VCH Verlag, 520-523.
  17. S. Oishi, T. Ogita, S. M. Rump, K. Tanabe: Accurate Cholesky Algorithm and Detection of Positive Definiteness of Ill-Conditioned Matrices, Proceedings of International Conference of Numerical Analysis and Applied Mathematics 2006, Crete, Greece, Wiley-VCH Verlag, 531-534.
  18. T. Ogita, S. Oishi: Fast Verification for Sparse Linear Systems with Generalized Diagonally Dominant Matrices, Proceedings of 2006 International Symposium on Nonlinear Theory and its Applications, Bologna, Italy, 2006, 319-321.
  19. S. Oishi, K. Tanabe, T. Ogita, S. M. Rump: Convergence Theorem of Rump's Method for Inverting Arbitrarily Ill-Conditioned Matrices, Proceedings of 2006 International Symposium on Nonlinear Theory and its Applications, Bologna, Italy, 2006, 315-318.
  20. K. Ozaki, T. Ogita, S. Oishi: Adaptive Verification Method for Dense Linear Systems, Proceedings of 2006 International Symposium on Nonlinear Theory and its Applications, Bologna, Italy, 2006, 323-326.
  21. T. Ohta, T. Ogita, S. M. Rump and S. Oishi: Numerical Verification Method for Dense Linear Systems with Arbitrarily Ill-conditioned Matrices, Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications, Bruges, Belgium, 2005, 745-748.
  22. K. Ozaki, T. Ogita, S. Miyajima, S. Oishi, S. M. Rump: Componentwise Verified Solutions of Linear Systems Suited for Java, Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications, Bruges, Belgium, 2005, 749-752.
  23. S. Miyajima, T. Ogita, S. Oishi: A Method of Generating Linear Systems with an Arbitrarily Ill-conditioned Matrix and an Arbitrary Solution, Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications, Bruges, Belgium, 2005, 741-744.
  24. S. Miyajima, T. Ogita, K. Ozaki, S. Oishi: Fast Error Estimation for Eigenvalues of Symmetric Matrix without Directed Rounding, Proceedings of the 2004 International Symposium on Nonlinear Theory and its Applications, Fukuoka, Japan, 2004, 167-170.
  25. T. Ogita, S. M. Rump, S. Oishi: Accurate Sum and Dot Product with Applications, Proceedings of the 2004 IEEE International Symposium on Computer Aided Control Systems Design, Taipei, Taiwan, 2004, 152-155.
  26. T. Ogita, S. Oishi, Y. Ushiro: Fast Verification of Solutions for Sparse Monotone Matrix Equations, Proceedings of the JSST 2000 International Conference on Modeling, Control and Computation in Simulation, Tokyo, Japan, 2000, 437-440.


[講究録・紀要・テクニカルレポート等 (Technical Report)]

  1. T. Ogita, K. Aishima: Iterative refinement for symmetric eigenvalue decomposition adaptively using higher-precision arithmetic, Mathematical Engineering Technical Reports (METR) 2016-11, 40 pages, The University of Tokyo, June 2016.
  2. Naoya Yamanaka, Tomoaki Okayama, Shin'ichi Oishi, Takeshi Ogita: A Fast Verified Automatic Integration Algorithm using Double Exponential Formula, 京大数理解析研究所講究録, 1638 (2009), 146-158.
  3. 荻田 武史, Siegfried M. Rump, 大石 進一: 大規模疎行列の正定値性の保証法, 京大数理解析研究所講究録, 1614 (2008), 34-39.
  4. 尾崎 克久, 荻田 武史, 大石 進一: 点と直線の位置関係の計算をロバストに行う点と平面の位置関係の精度保証法, 京大数理解析研究所講究録, 1614 (2008), 1-10.
  5. 荻田 武史, 尾崎 克久, 大石 進一: 行列式の高速な精度保証付き数値計算法, 京大数理解析研究所講究録, 1573 (2007), 45-52.
  6. S. M. Rump, T. Ogita, S. Oishi: Accurate Floating-Point Summation Part II: Sign, K-fold Faithful and Rounding to Nearest, Technical Report 07.2, Faculty for Information and Communication Sciences, Hamburg University of Technology, 2007.
  7. S. M. Rump, T. Ogita, S. Oishi: Accurate Floating-Point Summation Part I: Faithful Rounding, Technical Report 07.1, Faculty for Information and Communication Sciences, Hamburg University of Technology, 2007.
  8. S. M. Rump, T. Ogita, S. Oishi: Accurate Floating-point Summation, Technical Report 05.12, Faculty for Information and Communication Sciences, Hamburg University of Technology, 2005.
  9. 木村 欣司, 宮島 信也, 荻田 武史: 精度保証付き数値計算をつかったsuper fast real root counting, 数式処理, 12:2 (2005), 28-31.
  10. T. Ogita, S. M. Rump, S. Oishi: Verified Solutions of Linear Systems without Directed Rounding, Technical Report 2005-04, Advanced Research Institute for Science and Engineering, Waseda University, 2005.
  11. 木村 欣司，平野 照比古，荻田 武史，山澤 宏樹，曽我部 知広，横山 和弘: Real Root Countingに関する話題, 京大数理解析研究所講究録, 1456 (2005), 180-187.
  12. 尾崎 克久, 荻田 武史, 宮島 信也, 大石 進一: Javaによる連立一次方程式の数値解の精度保証法, 京大数理解析研究所講究録, 1441 (2005), 75-88.
  13. T. Ogita, S. M. Rump, S. Oishi: Accurate Sum and Dot Product, Technical Report 04.1, Faculty for Information and Communication Sciences, Hamburg University of Technology, 2004.
  14. 長谷川 秀彦, 曽我部 知広, 荻田 武史: 非対称行列から生成された対称行列に対するCG法, 京大数理解析研究所講究録, 1362 (2004), 6-12.
  15. 森山 敦史, 荻田 武史, 後 保範, 大石 進一: 拡張Strassen法による連立一次方程式の精度保証, 京大数理解析研究所講究録, 1362 (2004), 47-55.
  16. 藤坂 洋一, 中川 誠司, 荻田 武史, 外池 光雄: 不均質頭部モデルによる超音波領域骨導音波動伝搬解析, 信学技法 US2003-96 EA2003-126, 2004.
  17. 荻田 武史, 大石 進一, 後 保範: Strassenのアルゴリズムによる行列乗算の高速精度保証, 京大数理解析研究所講究録, 1320 (2003), 151-161.
  18. 荻田 武史, 後 保範, 大石 進一: 単調な疎行列における連立一次方程式の数値解の高速精度保証, 京大数理解析研究所講究録, 1198 (2001), 161-169.
  19. 荻田 武史, 後 保範: 有限要素法用ICCG法の並列化方法, 京大数理解析研究所講究録, 1145 (2000), 170-178.


[学位論文 (Ph.D. Thesis)]