Analysis of Some Padé-Chebyshev Approximants

Analysis of Some Padé-Chebyshev Approximants

We present some rational approximations of the sign function and analyze their convergence. The rate of convergence is shown to increase with the degree of the denominator of the rational approximation. Several numerical tests are presented.

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Veröffentlicht in:SIAM journal on numerical analysis 2006-01, Vol.43 (1), p.437-454
Hauptverfasser: Sidi Mahmoud Kaber, Maday, Yvon
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Approximations and expansions
Coefficients
Degrees of polynomials
Exact sciences and technology
Function discontinuity
Gibbs phenomenon
Mathematical analysis
Mathematical functions
Mathematics
Polynomials
Sciences and techniques of general use
Spectral methods
Uniqueness
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Zusammenfassung:We present some rational approximations of the sign function and analyze their convergence. The rate of convergence is shown to increase with the degree of the denominator of the rational approximation. Several numerical tests are presented.
ISSN:0036-1429
1095-7170