Quadrature formulas for matrix measures—a geometric approach

AbstractA geometric approach to quadrature formulas for matrix measures is presented using the relations between the representations of the boundary points of the moment space (generated by all matrix measures) and quadrature formulas. Simple proofs of existence and uniqueness of quadrature formulas of maximal degree of precision are given. Several new quadrature formulas for matrix measures supported on a compact interval are presented and several examples are discussed. Additionally, a special construction of degenerated quadrature formulas is discussed and some results regarding the location of the zeros of polynomials orthogonal with respect to a matrix measure on a compact interval are obtained as a by-product