Accurate solutions of product linear systems associated with rank-structured matrices
The author studies how to accurately solve linear systems whose coefficient matrices belong to the class of consecutive-rank-descending (CRD) matrices. The well-known Vandermonde and Cauchy matrices belong to the class CRD. A mechanism is proposed by which the inverse of any product of CRD matrices is generated in a subtraction-free way. Utilizing this method, solutions of linear systems corresponding to such products are accurately determined. Specifically, certain linear systems associated with products of Vandermonde and Cauchy matrices are solved to a high relative accuracy. An error analysis is presented and numerical experiments are provided as illustrations.
scientific article; zbMATH DE number 6989846
scientific article