Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T16:12:32.767Z Has data issue: false hasContentIssue false
  • English
  • Français

Computing values of a function on [0,1] from its moments

Published online by Cambridge University Press:  14 November 2011

Jet Wimp
Jet Wimp
Affiliation:
University of Strathclyde, Glasgow and Drexel University, Philadelphia, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Extract

In this work we present an algorithm for computing an integrable function almost everywhere on (0,1) when its moments are known. The method is based on the use of certain delta-shaped sequences, and can be adjusted to take advantage of the local smoothness of the function.

As an application, we give an algorithm for the pointwise inversion of the Laplace transform which utilizes the values of the image function at equidistant points.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 3-4 , 1979 , pp. 273 - 289
Copyright
Copyright © Royal Society of Edinburgh 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Widder, D. V.. The Inversion of the Laplace Integral and the Related Moment Problem. Trans. Amer. Math. Soc. 36 (1934), 107–200.CrossRefGoogle Scholar
2Olver, F. W. J.. Asymptotics and Special Functions (New York: Academic Press, 1974).Google Scholar
3Titchmarsh, E. C.. The Theory of Functions, 2nd edn (Oxford University Press, 1939).Google Scholar
4Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.. Higher Transcendental Functions (New York: McGraw Hill, 1954).Google Scholar
5Wimp, Jet. Recursion Formulae for Hypergeometric Functions. Math. Comput. 22 (1968), 363–373.Google Scholar
6Erddlyi, A.. Asymptotic Expansions (New York: Dover, 1956).Google Scholar
7Widder, D. V.. The Laplace Transform (Princeton Univ. Press, 1946).Google Scholar
8Shuvaev, A. K.. Delta Methods for Numerical Inversion of the Laplace Transform, and Their Convergence. J. Comp. Math. Math. Phys. 15 (1956), 22–32.CrossRefGoogle Scholar
9May, C. P.. Saturation and Inverse Theorems for Combinations of a Class of Exponential Type Operators. Can. J. Math. 28 (1976), 1224–1250.CrossRefGoogle Scholar
10Butzer, P. L.. Linear Combinations of Bernstein Polynomials. Can. J. Math. 5 (1953), 559–567.CrossRefGoogle Scholar