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

Autor: Kuniyoshi Abe, Soichiro Ikuno, Seiji Fujino

Publikováno v: Journal of Advanced Simulation in Science and Engineering. 6:128-140

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::1cfec17f6248a1a6decd51464e5f9011
https://doi.org/10.15748/jasse.6.128

Converting BiCR method for linear equations with complex symmetric matrices

Autor: Seiji Fujino, Kuniyoshi Abe

Publikováno v: Applied Mathematics and Computation. 321:564-576

The Bi-Conjugate Gradient (BiCG) method for Symmetric Complex matrices (SCBiCG), which can be derived from BiCG, has been proposed for solving linear equations with complex symmetric matrices. However, an alternative method derived from the Bi-Conjug

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ec8b3114bd078193744b94db585d7b12
https://doi.org/10.1016/j.amc.2017.10.046

Hybrid enriched bidiagonalization for discrete ill-posed problems

Autor: Per Christian Hansen, Kuniyoshi Abe, Yiqiu Dong

Publikováno v: Hansen, P C, Dong, Y & Abe, K 2019, ' Hybrid enriched bidiagonalization for discrete ill-posed problems ', Numerical Linear Algebra with Applications, vol. 26, no. 3, e2230 . https://doi.org/10.1002/nla.2230

The regularizing properties of the Golub–Kahan bidiagonalization algorithm are powerful when the associated Krylov subspace captures the dominating components of the solution. In some applications the regularized solution can be further improved by

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8b5705b2f087386fb0b5a2891559a1b9
https://orbit.dtu.dk/en/publications/0c0c0d90-5b1a-4a89-878c-1ee82c1d245b

On MrR (Mister R) Method for Solving Linear Equations with Symmetric Matrices

Autor: Kuniyoshi Abe, Seiji Fujino

Publikováno v: Communications in Computer and Information Science ISBN: 9789811065019

Krylov subspace methods, such as the Conjugate Gradient (CG) and Conjugate Residual (CR) methods, are treated for efficiently solving a linear system of equations with symmetric matrices. AZMJ variant of Orthomin(2) (abbreviated as AZMJ) [1] has rece

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::9a4615ba146d798695c3f9f59aa5fd4f
https://doi.org/10.1007/978-981-10-6502-6_45

A quasi-minimal residual variant of IDRstab using the residual smoothing technique

Autor: Emiko Ishiwata, Kuniyoshi Abe, Kensuke Aihara

Publikováno v: Applied Mathematics and Computation. 236:67-77

Quasi-Minimal Residual (QMR)-type methods have been developed for improving the oscillations in the residual norms of the Bi-Conjugate Gradient (Bi-CG) method and the hybrid Bi-CG methods. The IDRstab method, which combines the Induced Dimension Redu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::7a3fa54ef61f644a2dd4343d805be2d4
https://doi.org/10.1016/j.amc.2014.03.034