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Zbl 1170.65026
Sogabe, T.; Sugihara, M.; Zhang, S.-L.
An extension of the conjugate residual method to nonsymmetric linear systems. (English)
[J] J. Comput. Appl. Math. 226, No. 1, 103-113 (2009). ISSN 0377-0427

This paper adapts the conjugate residual method (CR) that solves large sparse symmetric systems to general sparse matrix systems. Special attention is paid to keep the computational effort constantly low per iteration, such as done with a two-sided Lanczos process in the bi-conjugate gradient method (Bi-CG) with short term recurrences. The paper describes and analyses the bi-conjugate gradient method in this light and extends conjugate residual to the new bi-conjugate residual algorithm (Bi-CR) for non-symmetric systems. The properties and convergence behavior of Bi-CR is studied and compared to Bi-CG. In experiments, Bi-CR appears to offer smoother and often faster convergence than Bi-CG.
[Frank Uhlig (Auburn)]

MSC 2000:: *65F10 Iterative methods for linear systems

Keywords: sparse linear system; conjugate gradient method; conjugate residual method; Krylov subspace method; bi-conjugate gradient method; numerical examples; nonsymmetric linear systems; Lanczos algorithm; coupled two-term recurrences; convergence

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Zentralblatt MATH Berlin [Germany]