GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
CGS, a fast Lanczos-type solver for nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Variants of BICGSTAB for matrices with complex spectrum
SIAM Journal on Scientific Computing
GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
A COCR method for solving complex symmetric linear systems
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
An extension of the conjugate residual method to nonsymmetric linear systems
Journal of Computational and Applied Mathematics
Lanczos-type variants of the COCR method for complex nonsymmetric linear systems
Journal of Computational Physics
The BiCOR and CORS Iterative Algorithms for Solving Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
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For solving nonsymmetric linear systems, we attempt to establish symmetric structures in nonsymmetric systems and handle them through the methods devised for symmetric cases. A Biconjugate A-Orthogonal Residual method based on Biconjugate A-Orthonormalization Procedure has been proposed and nominated as BiCOR in [Y.-F. Jing, T.-Z. Huang, Y. Zhang, L. Li, G.-H. Cheng, Z.-G. Ren, Y. Duan, T. Sogabe, B. Carpentieri, Lanczos-type variants of the COCR method for complex nonsymmetric linear systems, J. Comput. Phys. 228 (2009) 6376-6394.]. As many similar characteristics exist between BiCOR and BiCG, the strategies of improved variants of BiCG, such as CGS and BiCGSTAB, can be utilized to enhance the algorithm for BiCOR. Making use of the product of residual polynomials of BiCOR and other polynomials, CORS and BiCORSTAB have been proposed along the same ideas of CGS and BiCGSTAB, respectively in the above-mentioned paper. In this paper, a unified generalized framework of product-type BiCOR, which is epitomized by the product of residual polynomials and other polynomials, is proposed. Numerical examples are selected from the blurring signal cases and the effect of the generalized product-type BiCOR method is prominent in signal deconvolution.