Szegő-Lobatto quadrature rules
Szegö quadrature rules are analogs of Gauss quadrature rules for the integration of periodic functions. They integrate exactly trigonometric polynomials of as high degree as possible. Szegö quadrature rules have a free parameter, which can be used to prescribe one node. This paper discusses so-called Szegö-Lobatto rules, i.e., Szegö quadrature rules with 2 prescribed nodes. It is shown that Szegö-Lobatto rules exist and that, generally, they depend on a parameter which can be chosen on a circular arc. The nodes and weights of a Szegö-Lobatto rule are the eigenvalues and the squares of the first component of the normalized eigenvectors of a unitary upper Hessenberg matrix. The nodes and weights can be computed with software for the unitary eigenvalue problem for upper Hessenberg matrices.
scientific article; zbMATH DE number 5117671
scientific article