Abstract
The theory of strong moment problems has provided Gaussian quadrature rules for approximate integration with respect to strong distributions. In Hagler (Ph.D. Thesis, University of Colorado, Boulder, 1997) and Hagler et al. (Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, in press), a transformation of the form v( x)=(1/ λ)( x− γ/ x), λ, γ>0, is used to obtain strong mass distribution functions from mass distribution functions. This transformation also links the systems of orthogonal polynomials and Laurent polynomials and their zeros. In this paper we show how the transformation method can be used to obtain the Gaussian quadrature rules for strong extensions of mass distribution functions. We then provide numerical examples of strong Gaussian quadrature approximations to the integrals of elementary functions with respect to selected strong distributions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
