Abstract
Consider the Vandermonde-like matrix P:=(P k(x M,l)) l,k=0 M,N, where the polynomials P k satisfy a three-term recurrence relation and x M, l ∈[−1,1] are arbitrary nodes. If P k are the Chebyshev polynomials T k , then P coincides with A:=(T k(x M,l)) l=0,k=0 M,N. This paper presents a fast algorithm for the computation of the matrix–vector product Pa in O(N log 2N) arithmetical operations. The algorithm divides into a fast transform which replaces Pa with A a ̃ and a fast cosine transform on arbitrary nodes (NDCT). Since the first part of the algorithm was considered in [Math. Comp. 67 (1998) 1577], we focus on approximative algorithms for the NDCT. Our considerations are completed by numerical tests.
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