A Björck-Pereyra-type algorithm for Szegö-Vandermonde matrices based on properties of unitary Hessenberg matrices
The paper presents a Björk-Pereyra-type algorithm to solve linear systems with a polynomial-Vandermonde \(n\times n \) matrix, where the corresponding polynomials are the Szegö polynomials. Such matrix is called the Szegö-Vandermonde matrix. The algorithm exploits the properties of the related unitary Hessenberg matrix to reduce the computational complexity \(O(n^2)\) operations which is in contrast to the usual \(O(n^3)\) complexity of standard structure ignoring methods. Numerical experiments indicate a good performance for ill-conditioned systems when comparing it with the Gaussian elimination.
scientific article; zbMATH DE number 5083631
scientific article