Backward stability of Clenshaw's algorithm
The question of the effect of roundoff errors in applying \textit{C. W. Clenshaw}'s algorithm [A note on the summation of Chebyshev series. Math. Tables Aids Comput. 9, 118-120 (1955; Zbl 0065.05403)] for summing the series \(w=b_0p_0+b_1p_1+ \ldots +b_np_n\) where \(p_n\) satisfy the linear three-term recurrence relation has been studies. The author gives some sufficient conditions under which Clenshaw's algorithm is backward stable. And finally, he proves that under certain assumptions, Clenshaw's algorithm is backward stable with respect to the data \(b_n\), \(n=0,1 \dots,N.\)
scientific article; zbMATH DE number 1886392