Stability of parallel algorithms to evaluate Chebyshev series

✍ Scribed by R. Barrio

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 644 KB
• Volume: 41
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(01)00102-x

✦ Synopsis

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 forward error is also studied by means of a more direct approach that permits us to obtain sharper bounds. The bounds show an almost stable behavior as in the sequential algorithms. This fact is illustrated with several numerical tests. (~) 2001 Elsevier Science Ltd. All rights reserved.