Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



A fast Laplace transform based on Laguerre functions

Author: John Strain
Journal: Math. Comp. 58 (1992), 275-283
MSC: Primary 44A10; Secondary 33C45, 44-04, 65R10
MathSciNet review: 1106983
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we present a fast algorithm which evaluates a discrete Laplace transform with N points at M arbitrarily distributed points in $ C(N + M)$ work, where C depends only on the precision required. Our algorithm breaks even with the direct calculation at $ N = M = 20$, and achieves a speedup of 1000 with 10000 points. It is based on a geometric divide and conquer strategy, combined with the manipulation of Laguerre expansions via a dilation formula for Laguerre functions.

References [Enhancements On Off] (What's this?)

  • [1] E. D. Rainville, Special functions, Chelsea, New York, 1960. MR 0107725 (21:6447)
  • [2] V. Rokhlin, A fast algorithm for the discrete Laplace transformation, J. Complexity 4 (1988), 12-32. MR 939693 (89b:65309)
  • [3] G. Szegö, Orthogonal polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, RI, 1975.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 44A10, 33C45, 44-04, 65R10

Retrieve articles in all journals with MSC: 44A10, 33C45, 44-04, 65R10

Additional Information

Keywords: Laplace transform, fast algorithms, Laguerre polynomials
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society