Abstract
Numerous versions of the Lanczos τ-methods have been extensively used to produce polynomial approximations for functions verifying a linear differential equation with polynomial coefficients. In the case of an initial-value problem, an adapted τ-method based on Chebyshev series and the use of symbolic computation lead to a rational approximation of the solution on a region of the complex plane. Numerical examples show that the simplicity of the method does not prevent a high accuracy of results.
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Rebillard, L. Rational approximation in the complex plane using a τ-method and computer algebra. Numerical Algorithms 16, 187–208 (1997). https://doi.org/10.1023/A:1019143231331
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DOI: https://doi.org/10.1023/A:1019143231331