Stability of parallel algorithms to evaluate Chebyshev series

AbstractIn 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