VRP-IGMRES(m)algorithm based on incomplete orthogonalization

doi:10.3969/j.issn.1000-1565.2018.05.003

Abstract

Abstract: In order to solve large linear equations efficiently, based on the Generalized Minimal Residual with Variable Restart Parameter algorithm(VRP-GMRES(m)), a truncation-pattern Incomplete Generalized Minimal Residual with Variable Restart Parameter algorithm(VRP-IGMRES(m))is proposed using the truncation technology,namely, using incomplete orthogonal Arnoldi process to constructe the base vector of the Krylov subspace and the Hessenberg matrix. The convergence of the algorithm is proved by the relationship between the angle cosine and the modulus of the two successive iterated residual vectors. Finally, through numerical examples to analyze the influence of truncation index on computational accuracy and efficiency, it is found that VRP-IGMRES(m)algorithm can effectively improve the computation efficiency under the premise of guaranteeing the accuracy. The obtained optimal truncation ratio is about 0.1. Our work provides a new method for solving practical engineering problems.

Key words: VRP-IGMRES(m)algorithm, incomplete orthogonalization, optimal truncation ratio

CLC Number:

O242

HAO Xuejing, YU Chunxiao, REN Cuihuan. VRP-IGMRES(m)algorithm based on incomplete orthogonalization[J]. Journal of Hebei University (Natural Science Edition), 2018, 38(5): 460-465.

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