Gaussian quadrature formulae for matrix weights
The authors study Gaussian quadrature formulae for a matrix weight.The first part of the paper provides the construction of Gaussian quadrature formulae such that the sum of the rank of the quadrature matrix coefficients is a given nonegative integer.In this case the nodes are the eigenvalues of certain perturbation of the truncated N-Jacobi matrix.The quadrature coefficients in the partial fraction decomposition of the ratio between the inverse of the orthonormal matrix polynomial and the associated polynomial of second kind.In the second part, the authors prove that any Gaussian quadrature formula for matrix weight must be of the above form.
scientific article; zbMATH DE number 1864737
scientific article