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Selected Topics in Approximation and Computation$
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Marek A. Kowalski, Krzystof A. Sikorski, and Frank Stenger

Print publication date: 1995

Print ISBN-13: 9780195080599

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195080599.001.0001

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Explicit Sinc-Like Methods

Explicit Sinc-Like Methods

(p.153) Chapter 4 Explicit Sinc-Like Methods
Selected Topics in Approximation and Computation

Marek A. Kowalski

Krzysztof A. Sikorski

Frank Stenger

Oxford University Press

In this section we derive several methods of approximation using the function values {f(kh)}∞k=- ∞ . We present a family of simple rational functions, which make possible the explicit and arbitrarily accurate rational approximation of the filter, the step (Heaviside) and the impulse (delta) functions. The chief advantage of these methods is that they make it possible to write down a simple and explicit rational approximation corresponding to any desired accuracy. Also, the three families of approximations are very simply connected with one another—the filter being related to the Heaviside via an elementary transformation, and the impulse being the derivative of the Heaviside. Thus, these methods make it possible for us to approximate generalized functions. In this section we discuss various methods, some of which are new, for approximating a function f ( t ) using the values f(0), f(±h), f(±2h), . .., where h > 0.

Keywords:   Bromwich’s inversion formula, Heaviside function, Poisson’s summation formula, delta function, filter function, impulse function

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