In this paper, we analyse the stability of parallel algorithms for the evaluation of polynomials written as a finite series of orthogonal polynomials. The basic part of the computation is the solution of a triangular tridiagonal linear system. This fact allows us to present a more detailed analysis. The theoretical results show that the parallel algorithms are almost as stable as their sequential counterparts for practical applications. Extensive numerical experiments confirm the theoretical conclusions.
Barrio, R., & Yalamov, P. (2003). Stability of parallel algorithms for polynomial evaluation. Computers and Mathematics with Applications, 46(5–6), 769–781. https://doi.org/10.1016/S0898-1221(03)90140-4