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Restricted Padé Approximations to the Exponential Function

1978; Society for Industrial and Applied Mathematics; Volume: 15; Issue: 5 Linguagem: Inglês

10.1137/0715066

1095-7170

Syvert P. Nørsett,

Iterative Methods for Nonlinear Equations

In the rational Pade approximation to exp $\exp ( - q),q \in \mathbb{C}$, the parameters in the numerator and denominator are chosen to give maximum order. The zeros of the denominator of these approximations are distinct with at most one being real. When solving stiff systems, some methods have a close relation to rational approximations to $\exp ( - q)$ where the denominator is a repeated real linear factor. This paper is concerned with some general questions about approximations of this kind to $\exp ( - q)$. Existence, nonuniqueness, smallest error constant and convergence are discussed.