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Roundoff error analysis of the fast cosine transform and its application to the Chebyshev pseudospectral method. (English) Zbl 0823.65147

Authors’ abstract: The roundoff error of several algorithms commonly used to compute the fast cosine transform and the derivatives using the Chebyshev pseudospectral method is studied. We derive precise expressions for the algorithmic error, give new theoretical upper bounds and a statistical analysis. The results are compared with numerical experiments.

MSC:

65T50 Numerical methods for discrete and fast Fourier transforms
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65G50 Roundoff error
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