CQLW - A PACKAGE OF SUBROUTINES FOR POLYNOMIALS ORTHOGONAL WITH RESPECT TO ln(1/x), INCLUDING THEORY AND APPLICATIONS

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Authors
  1. Dawson, T.W.
Corporate Authors
Defence Research Establishment Pacific, Victoria BC (CAN)
Abstract
The main thrust of this document is an improved method for computing polynomials {A sub n (x)} orthogonal with respect to the positive weight functio n ln(1/x) on the interval epsilion (0,1). An implementation of Wheeler's algorithm was recently published in Numerical Recipes. However, the modified moments used are prone to underflow on computers with limited precision and floating-point range. The problems can be circumvented by employing scaling, and by working in terms of ratios. The paper contains a summary of general orthogonal polynomial theory, including a derivation of functional approximation and Gaussian quadrature from a matrix theory viewpoint. Subsequently, a derivation of Wheeler's algorithm, together with the two variations mentioned above, is presented. Appendix A documents a set of FORTRAN routines implementing the theory, including routines for evaluating the recursion coefficients, polynomial values and derivatives, points and weights for Gaussian quadrature, integrating scalar- and vector-valued functions, and approximating functions in series of these orthogonal polynomials.
Keywords
SYMBOLIC ALGEBRA SOFTWARE
Report Number
DREP-TM-94-108 — Technical Memorandum
Date of publication
01 Jun 1994
Number of Pages
56
DSTKIM No
95-00064
CANDIS No
143688
Format(s):
Hardcopy;Document Image stored on Optical Disk

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