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Proposal of new iterative scheme in GMRES
Author(s) -
Sato Shuji,
Yonekawa Tooru,
Murase Hiroshi
Publication year - 1998
Publication title -
electrical engineering in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.136
H-Index - 28
eISSN - 1520-6416
pISSN - 0424-7760
DOI - 10.1002/(sici)1520-6416(199806)123:4<15::aid-eej3>3.0.co;2-r
Subject(s) - generalized minimal residual method , residual , mathematics , iterative method , norm (philosophy) , matrix (chemical analysis) , computer science , algorithm , chemistry , chromatography , political science , law
In the paper, GMRES is applied to various large matrices appearing in 3D field analyses. By changing the condition of the matrices, effective preconditioning of the matrix is sought. Also studied is a relationship between the residual norm and the precision evaluated during GMRES. The paper shows that the residual norm, which is indirectly computed in GMRES and has so far been used as a measure of precision, cannot be used as an indicator of the solution's accuracy. After discussing deterioration of precision, GMRES(m1), which solves matrices with a modified iterative scheme, is proposed. It is to be confirmed that GMRES(m1) is faster and more accurate than any of GMRES and its modified version, GMRES(m). © 1998 Scripta Technica, Electr Eng Jpn, 123(4): 15–24, 1998