Gauss–Laurent-type quadrature rules for the approximation of functionals of a nonsymmetric matrix

This paper is concerned with the approximation of matrix functionals of the form w T f ( A ) v , where A ∈ ℝ n × n is a large nonsymmetric matrix, w , v ∈ ℝ n , and f is a function such that f ( A ) is well defined. We derive Gauss–Laurent quadrature rules for the approximation of these functionals, and also develop associated anti-Gauss–Laurent quadrature rules that allow us to estimate the quadrature error of the Gauss–Laurent rule. Computed examples illustrate the performance of the quadrature rules described.