Proposal of new iterative scheme in GMRES
Abstract
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
