Gauss-type quadrature rule with complex nodes and weights for integrals involving Daubechies scale functions and wavelets

摘要

This paper deals with derivation of a Gauss-type quadrature rule (named as GaussDaubechies quadrature rule) for numerical evaluation of integrals involving product of integrable function and Daubechies scale functions/wavelets. Some of the nodes and weights of the quadrature formula may be complex and appear with their conjugates. This is in contrast with the standard Gauss-type quadrature rule for integrals involving products of integrable functions and non-negative weight functions. This quadrature rule has accuracy as good as the standard Gauss-type quadrature rule and is also found to be stable. The efficacy of the quadrature rule derived here has been tested through some numerical examples. (C) 2015 Elsevier B.V. All rights reserved.