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Home/Magazine Archive/November 1973 (Vol. 16, No. 11)/A recurrence scheme for converting from one orthogonal.../Abstract

A recurrence scheme for converting from one orthogonal expansion into another

By Herbert E. Salzer
Communications of the ACM, November 1973, Vol. 16 No. 11, Pages 705-707
10.1145/355611.362548
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A generalization of a scheme of Hamming for converting a polynomial Pn(x) into a Chebyshev series is combined with a recurrence scheme of Clenshaw for summing any finite series whose terms satisfy a three-term recurrence formula. An application to any two orthogonal expansions Pn(x) = ∑nm=0 amqm(x) = ∑nm=0 AmQm(x) enables one to obtain Am directly from am, m = 0(1)n, by a five-term recurrence scheme.

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