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Parallel evaluation of Chebyshev and trigonometric series

✍ Scribed by R. Barrio; J. Sabadell

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
427 KB
Volume
38
Category
Article
ISSN
0898-1221

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In this paper, we present rounding error bounds of recent parallel versions of Forsythe's and Clenshaw's algorithms for the evaluation of finite series of Chebyshev polynomials of-the first and second kind. The backward errors are studied by using the matrix formulation of the algorithm, whereas the

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## Abstract Closed formulas are presented for a number of trigonometric series whose summands contain inverse powers of one or two quadratic forms. It is shown how to arrange the formulas to remove apparent numerical instabilities, and useful numerical approximations are identified together with th