Don, Wai Sun; Solomonoff, Alex Accuracy and speed in computing the Chebyshev collocation derivative. (English) Zbl 0840.65010 SIAM J. Sci. Comput. 16, No. 6, 1253-1268 (1995). The authors discuss Chebyshev collocation methods and study several algorithms for computing Chebyshev spectral derivatives. Then they describe a preconditioning method for reducing the roundoff error. By means of a statistical approach they estimate the minimum possible roundoff error.Using different algorithms they obtain some results on the accuracy of computing. The numerical errors associated with computing the elements of the differentiation matrix are described. They find out that if the entries of the matrix are computed accurately, then the roundoff error of the matrix-vector multiplication is as small as that obtained by the transform-recursion algorithm. For most practical grid sizes used in computations, the even-odd decomposition algorithm is found to be faster than the transform-recursion method. Reviewer: D.D.Stancu (Cluj-Napoca) Cited in 62 Documents MSC: 65D25 Numerical differentiation 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 65Y20 Complexity and performance of numerical algorithms 65F30 Other matrix algorithms (MSC2010) 65G50 Roundoff error Keywords:fast Fourier transform; Chebyshev collocation methods; Chebyshev spectral derivatives; preconditioning; roundoff error; differentiation matrix; matrix-vector multiplication; transform-recursion algorithm PDF BibTeX XML Cite \textit{W. S. Don} and \textit{A. Solomonoff}, SIAM J. Sci. Comput. 16, No. 6, 1253--1268 (1995; Zbl 0840.65010) Full Text: DOI Link OpenURL