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On the errors incurred calculating derivatives using Chebyshev polynomials. (English) Zbl 0747.65009

The round-off errors arising from the computation of derivatives of functions approximated by Chebyshev polynomials are studied on an example function. It is found that the error grows as \(N^ 2\) for standard Chebyshev transform methods, where \(N+1\) is the number of Chebyshev polynomials used to approximate the function.
It is also shown that matrix multiplication techniques exhibit errors of the same order of magnitude but the computation of the matrix elements is ill-conditioned (errors grow as \(N^ 2\)). The errors are most severe near the boundaries of the domain. A method for reducing the error is discussed.

MSC:

65D25 Numerical differentiation
65F30 Other matrix algorithms (MSC2010)
65G50 Roundoff error
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References:

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