Volume 25, pp. 17-26, 2006.

Alternative orthogonal polynomials and quadratures

Vladimir S. Chelyshkov

Abstract

A bidirectional orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0, 1] with the weighting function 1. Functional and recurrent relations are derived for the sequences that are the result of inverse orthogonalization procedure. Quadratures, generating by the sequences, are described. An example on approximation of the Cauchy problem is given.

Full Text (PDF) [183 KB]

Key words

orthogonal polynomial, recurrence relation, quadrature, initial value problem

AMS subject classifications

33C45

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