Rational approximation in the complex plane using a τ-method and computer algebra |
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Authors: | Rebillard Luc |
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Affiliation: | (1) Laboratoire LMC-IMAG, 51, Rue des Mathématiques, F-38031 Grenoble Cedex 9, France |
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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. This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | Chebyshev series initial value problems ordinary differential equation polynomial and rational approximation of functions τ -method 42C10 65D99 65L05 |
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