Art

J-GLOBAL ID：201902229520586949   Reference number：19A1744024

A Numerical Study for MrR Algorithm for Linear Equations with Symmetric Matrices

対称行列を伴う線形方程式に対するMrRアルゴリズムのための数値的研究

Author (3)： Abe Kuniyoshi (Faculty of Economics and Information, Gifu Shotoku University) ,  Fujino Seiji (Professor Emeritus, Kyushu University) ,  Ikuno Soichiro (School of Computer Science, Tokyo University of Technology)
Material： Journal of Advanced Simulation in Science and Engineering (Web)  (日本シミュレーション学会英文誌(Web))
Volume： 6  Issue： 1  Page： 128-140(J-STAGE)  Publication year： 2019 
JST Material Number： U0612A  ISSN： 2188-5303  Document type： Article
Article type： 原著論文  Country of issue： Japan (JPN)  Language： ENGLISH (EN)

Thesaurus term： *linear equation ,  *numerical solution ,  *matrix (mathematics) ,  algorithm ,  experiment ,  numerical calculation ,  symmetric matrix ,  numerical experiment
Semi thesaurus term： linear equation ,  Krylov subspace method ,  method of residuals ,  共役残差法

Author keywords (5)： Linear equations ,  Krylov subspace methods ,  Conjugate residual method ,  Symmetric matrices ,  Rutishauser

JST classification (1)： Numerical computation  (JE02000J)

Reference (16)：

• [1] K. Abe, S.-L. Zhang, T. Mitsui, C.-H. Jin: A variant of the Orthomin(2) method for singular linear systems, Numer. Algorithms, 36 (2004), 189-202.
• [2] K. Abe, S.-L. Zhang, T. Mitsui: MRTR method: An iterative method based on the three-term recurrence formula of CG-type for nonsymmetric matrix, Transactions of the Japan SIAM, 7 (1997), 37-50 (in Japanese).
• [3] M. R. Hestenes, E. L. Stiefel: Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards, 49 (1952), 409-435.
• [4] E. L. Stiefel: Relaxationsmethoden bester strategie zur losung linearer gleichungssysteme, Commentarii Mathematici Helvetici, 29 (1955), 157-179.
• [5] E. L. Stiefel: Kernel polynomial in linear algebra and their numerical applications, in: Further contributions to the determination of eigenvalues, NBS Applied Math. Ser., 49 (1958), 1-22.

Terms in the title (5)： 対称行列 ,  線形方程式 ,  アルゴリズム ,  数値 ,  研究