Generalization of the residual cutting method based on the Krylov subspace
Toshihiko Abe, Yoshihito Sekine, Kazuo Kikuchi · AIP conference proceedings · 2016
The residual cutting (RC) method has been reported to have superior converging characteristics in numerically solving elliptic partial differential equations. However, its application is limited to linear problems with diagonal-dominant matrices in general, for which convergence of a relaxation method such as SOR is guaranteed. In this study, we propose the generalized residual cutting (GRC) method, which is based on the Krylov subspace and applicable to general unsymmetric linear problems. Also, we perform numerical experiments with various coefficient matrices, and show that the GRC method has some desirable properties such as convergence characteristics and memory usage, in comparison to the conventional RC, BiCGSTAB and GMRES methods.At the request of the author of this paper, a corrigendum was issued on 22 June 2016 to correct an error in Eq. (2) and Eq. (3).