Backward Stability of Clenshaw's Algorithm |
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| Authors: | Alicja Smoktunowicz |
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| Institution: | (1) Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland |
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| Abstract: | We study numerical properties of Clenshaw's algorithm for summing the series w = 
n = 0
N
b
n
p
n
where p
n
satisfy the linear three-term recurrence relation. We prove that under natural assumptions Clenshaw's algorithm is backward stable with respect to the data b
n, n = 0,N. |
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| Keywords: | Numerical stability Chebyshev polynomials orthogonal polynomials condition number |
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