Abstract
For any given n-by- n matrix A n , T. Chan’s circulant preconditioner c F ( A n ) proposed by T. Chan [T. Chan, An optimal circulant preconditioner for Toeplitz systems, SIAM J. Sci. Statist. Comput. 9 (1988) 766–771] is defined to be the solution of min C n A n - C n ‖ F over all n-by- n circulant matrices C n . The c F ( A n ), called the optimal circulant preconditioner by T. Chan, has been proved to be a good preconditioner for a large class of structured systems. A generalization of T. Chan’s circulant preconditioner was given by Huckle [T. Huckle, Circulant and skew circulant matrices for solving Toeplitz matrix problems, SIAM J. Matrix Anal. Appl. 13 (1992) 767–777] which can be used for solving some general linear systems. In this paper, we review some old and develop some new properties of T. Chan’s circulant preconditioner.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
