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 wTf(A)v, where $A\in \mathbb {R}^{n\times n}$ is a large nonsymmetric matrix, $\boldsymbol {w},\boldsymbol {v}\in \mathbb {R}^{n}$ , 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.