The bad truth about Laplace's transform

被引：85

作者：

Epstein, Charles L. ^{[1
]}

Schotland, John ^{[2
]}

机构：

[1] Univ Penn, Dept Math, Philadelphia, PA 19104 USA

[2] Univ Penn, Dept Bioengn, Philadelphia, PA 19104 USA

来源：

SIAM REVIEW | 2008年 / 50卷 / 03期

关键词：

finite Fourier transform; FFT; Laplace transform; spectral theory; SVD; regularized inverse;

D O I：

10.1137/060657273

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Inverting the Laplace transform is a paradigm for exponentially ill-posed problems. For a class of operators, including the Laplace transform, we give forward and inverse formulae that have fast implementations using the fast Fourier transform. These formulae lead easily to regularized inverses whose effects on noise and filtered data can be precisely described. Our results give cogent reasons for the general sense of dread most mathematicians feel about inverting the Laplace transform.

引用

页码：504 / 520

页数：17

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