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Mathematics of Computation

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An implementation of Christoffel’s theorem in the theory of orthogonal polynomials

Author: David Galant
Journal: Math. Comp. 25 (1971), 111-113
MSC: Primary 65.55
MathSciNet review: 0288954
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Abstract: An algorithm for the construction of the polynomials associated with the weight function $w(t)P(t)$ from those associated with $w(t)$ is given for the case when $P(t)$ is a polynomial which is nonnegative in the interval of orthogonality. The relation of the algorithm to the LR algorithm is also discussed.

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Keywords: Numerical construction of orthogonal polynomials, quotient-difference algorithm, <I>LR</I> algorithm, Gaussian quadrature, three-term recurrence relations for orthogonal polynomials
Article copyright: © Copyright 1971 American Mathematical Society