精度保証に関する論文

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精度保証に関する論文

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「数値線形代数」の記事における「精度保証に関する論文」の解説

^ Yamamoto, T. (1984). Error bounds for approximate solutions of systems of equations. Japan Journal of Applied Mathematics, 1(1), 157. ^ Oishi, S., & Rump, S. M. (2002). Fast verification of solutions of matrix equations. en:Numerische Mathematik, 90(4), 755-773. ^ 森倉悠介, 椋木大地, 深谷猛, 山中脩也, & 大石進一. (2016). 大規模並列計算機における連立一次方程式の精度保証付き数値計算に対する性能評価. 研究報告ハイパフォーマンスコンピューティング (HPC), 2016(1), 1-7. ^ Kobayashi, Y., Ogita, T., & Ozaki, K. (2017). Acceleration of a preconditioning method for ill-conditioned dense linear systems by use of a BLAS-based method. Reliable Computing, 25, 15-23. ^ Kobayashi, Y., & Ogita, T. (2016). Accurate and efficient algorithm for solving ill-conditioned linear systems by preconditioning methods. Nonlinear Theory and Its Applications, IEICE, 7(3), 374-385. ^ A fast and efficient algorithm for solving ill-conditioned linear systems (JSIAM Letters Vol.7 (2015) pp.1-4) Yuka Kobayashi, Takeshi Ogita. ^ 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 Vol.15, No.3, 2005, pp.269-286, 太田貴久, 荻田武史, Siegfried M. Rump, 大石進一. ^ Yanagisawa, Y., Ogita, T., & Oishi, S. (2014). Convergence analysis of an algorithm for accurate inverse Cholesky factorization. Japan Journal of Industrial and Applied Mathematics, 31(3), 461-482. ^ Yanagisawa, Y., Ogita, T., & Oishi, S. I. (2014). A modified algorithm for accurate inverse Cholesky factorization. Nonlinear Theory and Its Applications, IEICE, 5(1), 35-46. ^ Yanagisawa, Y., & Ogita, T. (2013). Convergence analysis of accurate inverse Cholesky factorization. JSIAM Letters, 5, 25-28. ^ Minamihata, A., Sekine, K., Ogita, T., Rump, S. M., & Oishi, S. I. (2015). Improved error bounds for linear systems with H-matrices. Nonlinear Theory and Its Applications, IEICE, 6(3), 377-382. ^ Rump, S. M., & Ogita, T. (2007). Super-fast validated solution of linear systems. en:Journal of computational and applied mathematics, 199(2), 199-206. ^ Yamamoto, T. (1980). Error bounds for computed eigenvalues and eigenvectors. en:Numerische Mathematik, 34(2), 189-199. ^ Yamamoto, T. (1982). Error bounds for computed eigenvalues and eigenvectors. II. en:Numerische Mathematik, 40(2), 201-206. ^ Mayer, G. (1994). Result verification for eigenvectors and eigenvalues. Topics in Validated Computations, Elsevier, Amsterdam, 209-276. ^ Rump, S. M. (1994). Verification methods for dense and sparse systems of equations. ^ Rump, S. M. (2001). Computational error bounds for multiple or nearly multiple eigenvalues. Linear Algebra and its Applications, 324(1-3), 209-226. ^ Rump, S. M., & Zemke, J. P. M. (2003). On eigenvector bounds. en:BIT Numerical Mathematics, 43(4), 823-837. ^ Yamamoto, N. (2001). A simple method for error bounds of eigenvalues of symmetric matrices. Linear Algebra and its Applications, 324(1-3), 227-234. ^ Elsner, L., & Friedland, S. (1995). Singular values, doubly stochastic matrices, and applications. Linear Algebra and Its Applications, 220, 161-169. ^ Ipsen, I. C. (1998). Relative perturbation results for matrix eigenvalues and singular values. en:Acta numerica, 7, 151-201. ^ Deif, A. S. (1990). Realistic apriori and a posteriori error bounds for computed eigenvalues. IMA journal of numerical analysis, 10(3), 323-329. ^ 丸山晃佐, 荻田武史, 中谷祐介, & 大石進一. (2004). 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 A, 87(8), 1111-1119. ^ Alefeld, G., Gienger, A., & Mayer, G. (1994). Numerical validation for an inverse matrix eigenvalue problem. Computing, 53(3-4), 311-322. ^ Miyajima, S. (2017). Verified Solutions of Inverse Symmetric Eigenvalue Problems. Reliable Computing, 24(1), 31-44. ^ Demmel, J., & Kahan, W. (1990). Accurate singular values of bidiagonal matrices. SIAM Journal on Scientific and Statistical Computing, 11(5), 873-912. ^ Oishi, S. (2001). Fast enclosure of matrix eigenvalues and singular values via rounding mode controlled computation. Linear algebra and its Applications, 324(1-3), 133-146. ^ 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(数値シミュレーションを支える応用数理)」『数理解析研究所講究録』第1573号、京都大学数理解析研究所、2007年、 45-52頁、 ISSN 18802818、 NAID 110006446072。 ^ Ogita, T. (2008). Verified Numerical Computation of Matrix Determinant. SCAN’2008 El Paso, Texas September 29–October 3, 2008, 86. ^ 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 Vol.21, No.3, 2011, pp.186–196, 尾崎克久, 荻田武史, 大石進一. ^ 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 (微分方程式の数値解法と線形計算)」『数理解析研究所講究録』第1320号、京都大学数理解析研究所、2003年、 151-161頁、 ISSN 1880-2818、 NAID 110000167325。 ^ 宮島信也「行列方程式の解に対する数値的検証法の進展」『応用数理』第29巻第2号、日本応用数理学会、2019年、 18-25頁、 doi:10.11540/bjsiam.29.2_18、 NAID 130007720875。 ^ Shinya Miyajima, Verified computation for the Hermitian positive definite solution of the conjugate discrete-time algebraic Riccati equation, en:Journal of Computational and Applied Mathematics, Volume 350, Pages 80-86, April 2019. ^ inya Miyajima, Fast verified computation for the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation, Computational and Applied Mathematics, Volume 37, Issue 4, Pages 4599-4610, September 2018. ^ Shinya Miyajima, Fast verified computation for the solution of the T-congruence Sylvester equation, Japan Journal of Industrial and Applied Mathematics, Volume 35, Issue 2, Pages 541-551, July 2018. ^ Shinya Miyajima, Fast verified computation for the solvent of the quadratic matrix equation, The Electronic Journal of Linear Algebra, Volume 34, Pages 137-151, March 2018 ^ Shinya Miyajima, Fast verified computation for solutions of algebraic Riccati equations arising in transport theory, Numerical Linear Algebra with Applications, Volume 24, Issue 5, Pages 1-12, October 2017. ^ Shinya Miyajima, Fast verified computation for stabilizing solutions of discrete-time algebraic Riccati equations, en:Journal of Computational and Applied Mathematics, Volume 319, Pages 352-364, August 2017. ^ Shinya Miyajima, Fast verified computation for solutions of continuous-time algebraic Riccati equations, Japan Journal of Industrial and Applied Mathematics, Volume 32, Issue 2, Pages 529-544, July 2015. ^ Miyajima, S. (2019). Verified computation of the matrix exponential. Advances in Computational Mathematics, 45(1), 137-152. ^ Miyajima, S. (2019). Verified computation for the matrix principal logarithm. Linear Algebra and its Applications, 569, 38-61. ^ Miyajima, S. (2018). Fast verified computation for the matrix principal pth root. en:Journal of Computational and Applied Mathematics, 330, 276-288.