A generalized product-type BiCOR method and its application in signal deconvolution

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.