Stability of parallel algorithms to evaluate Chebyshev series
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 uf 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 all almost stable behavior as ill the sequential algorithms. This fact is: illustrated with several numerical tests. (C) 2001 Elsevier Science Ltd. All rights reserved.
parallel algorithms roundoff error polynomial evaluation