Abstract
The main result is the “black dot algorithm” and its fast version for the construction of a new circulant preconditioner for Toeplitz matrices. This new preconditioner C is sought directly as a solution to one of possible settings of the approximation problem A ≈ C + R, where A is a given matrix and R should be a “low-rank” matrix. This very problem is a key to the analysis of superlinear convergence properties of already established circulant and other matrix-algebra preconditioners. In this regard, our new preconditioner is likely to be the best of all possible circulant preconditioners. Moreover, in contrast to several “function-based” circulant preconditioners used for “bad” symbols, it is constructed entirely from the entries of a given matrix and performs equally as the best of the known or better than those for the same symbols.
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.
