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

• M.M. Panja ^[2] ; B.N. Mandal ^[1]
  1. [1] Indian Statistical Institute

     Indian Statistical Institute

     India

     
  2. [2] Visva-Bharati, Santiniketan, India
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 290, Nº 1, 2015, págs. 609-632
• Idioma: inglés
• DOI: 10.1016/j.cam.2015.05.024
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• Resumen

  • This paper deals with derivation of a Gauss-type quadrature rule (named as Gauss–Daubechies 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.