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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Complex variable and regularization methods of inversion of the Laplace transform
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by D. D. Ang, John Lund and Frank Stenger PDF
Math. Comp. 53 (1989), 589-608 Request permission


In this paper three methods are derived for approximating f, given its Laplace transform g on $(0,\infty )$, i.e., $\smallint _0^\infty {f(t)\exp ( - st) dt = g(s)}$. Assuming that $g \in {L^2}(0,\infty )$, the first method is based on a Sinc-like rational approximation of g, the second on a Sinc solution of the integral equation $\smallint _0^\infty {f(t)\exp ( - st) dt = g(s)}$ via standard regularization, and the third method is based on first converting $\smallint _0^\infty {f(t)\exp ( - st){\mkern 1mu} dt = g(s)}$ to a convolution integral over $\mathbb {R}$, and then finding a Sinc approximation to f via the application of a special regularization procedure to solve the Fourier transform problem. We also obtain bounds on the error of approximation, which depend on both the method of approximation and the regularization parameter.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 589-608
  • MSC: Primary 65R10; Secondary 44A10
  • DOI:
  • MathSciNet review: 983558