On a class of Gauss-like quadrature rules
Numerische Mathematik
Vector orthogonal polynomials of dimension−d
Proceedings of the conference on Approximation and computation : a fetschrift in honor of Walter Gautschi: a fetschrift in honor of Walter Gautschi
Proceedings of the international conference (dedicated to Thomas Jan Stieltjes, Jr.) on Orthogonality, moment problems and continued fractions
Algebraic aspects of matrix orthogonality for vector polynomials
Journal of Approximation Theory
Numerical analysis: an introduction
Numerical analysis: an introduction
Multiple orthogonal polynomials
Journal of Computational and Applied Mathematics
Some classical multiple orthogonal polynomials
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. V: quadrature and orthogonal polynomials
Some discrete multiple orthogonal polynomials
Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Hermite-Padé approximation and simultaneous quadrature formulas
Journal of Approximation Theory
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We study multiple orthogonal polynomials of type I and type II, which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the eigenvalue problem of a banded lower Hessenberg matrix L"n, containing the recurrence coefficients. As a consequence, we easily find that the multiple orthogonal polynomials of type I and type II satisfy a generalized Christoffel-Darboux identity. Furthermore, we explain the notion of multiple Gaussian quadrature (for proper multi-indices), which is an extension of the theory of Gaussian quadrature for orthogonal polynomials and was introduced by Borges. In particular, we show that the quadrature points and quadrature weights can be expressed in terms of the eigenvalue problem of L"n.