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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
DOI: https://doi.org/10.1090/S0025-5718-1971-0288954-8
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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DOI: https://doi.org/10.1090/S0025-5718-1971-0288954-8
Keywords: Numerical construction of orthogonal polynomials, quotient-difference algorithm, LR algorithm, Gaussian quadrature, three-term recurrence relations for orthogonal polynomials
Article copyright: © Copyright 1971 American Mathematical Society

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