On computing modified moments for half-range Hermite weights

Abstract

In this paper we consider the computation of the modified moments for the system of Laguerre polynomials on the real semiaxis with the Hermite weight. These moments can be used for the computation of integrals with the Hermite weight for the real semiaxis, either via product rules or via the construction of the n-point Gaussian quadrature rule with respect to this nonstandard weight using the Chebyshev algorithm. We propose a new computational method based on the construction of the null-space of a rectangular matrix derived from the three--term recurrence relation of the system of orthonormal Laguerre polynomials. It is shown that the proposed algorithm computes the modified moments with high accuracy and linear complexity. Numerical examples illustrate the effectiveness of the proposed method.