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Zbl 0840.65010
Don, Wai Sun; Solomonoff, Alex
Accuracy and speed in computing the Chebyshev collocation derivative. (English)
[J] SIAM J. Sci. Comput. 16, No.6, 1253-1268 (1995). ISSN 1064-8275; ISSN 1095-7197/e

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.\par 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.
[D.D.Stancu (Cluj-Napoca)]

MSC 2000:: *65D25 Numerical differentiation
65N35 Collocation methods (BVP of PDE)
65Y20 Complexity and performance of numerical algorithms
65F30 Other matrix algorithms
65G50 Roundoff error

Keywords: fast Fourier transform; Chebyshev collocation methods; Chebyshev spectral derivatives; preconditioning; roundoff error; differentiation matrix; matrix-vector multiplication; transform-recursion algorithm

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