Abstract
In this paper, we consider how to accurately solve linear systems associated with a wide class of rank-structured matrices containing the well-known Vandermonde and Cauchy matrices, i.e., consecutive-rank-descending (CRD) matrices. We provide a mechanism to guarantee that the inverse of any product of CRD matrices is generated in a subtraction-free manner. With the mechanism, the solutions of linear systems associated with such products are accurately determined by the parameters of CRD factors, and we then accurately compute the solutions as warranted by these parameters. In particular, linear systems associated with products of Vandermonde and Cauchy matrices, whose nodes satisfy certain positive or negative properties, are solved to high relative accuracy. Error analysis and numerical experiments are provided to confirm the high accuracy.
Sign-in/Register to access full text options 
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.
