ON THE REGULARIZED INVERSION OF THE LAPLACE TRANSFORM

被引：34

作者：

BRIANZI, P ^{[1
]}

FRONTINI, M ^{[1
]}

机构：

[1] POLITECN MILAN,DIPARTMENTO MATEMAT,I-20133 MILAN,ITALY

来源：

INVERSE PROBLEMS | 1991年 / 7卷 / 03期

关键词：

D O I：

10.1088/0266-5611/7/3/004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we present an algorithm for the regularized inversion of the Laplace transform. We assume that the values of the Laplace transform are given in a finite number of equidistant points rho-i and that these values are affected by a Gaussian random noise with zero expectation and standard deviation sigma. The algorithm is applied to several examples and, in general, it gives a good approximation of the normal solution; numerical results are presented for values of sigma in the range [10-(6), 10(-2)] and for sigma = 0 (no noise).

引用

页码：355 / 368

页数：14

共 19 条

[1]

BELLMANN R, 1966, NUMERICAL INVERSION

[2] LINEAR INVERSE PROBLEMS WITH DISCRETE-DATA .1. GENERAL FORMULATION AND SINGULAR SYSTEM-ANALYSIS [J].

BERTERO, M ;

DEMOL, C ;

PIKE, ER .

INVERSE PROBLEMS, 1985, 1 (04) :301-330

[3]

BERTERO M, 1983, PUBBLICAZIONI I ANAL, V11

[4] IMPROVED ESTIMATES OF STATISTICAL REGULARIZATION PARAMETERS IN FOURIER DIFFERENTIATION AND SMOOTHING [J].

DAVIES, AR ;

ANDERSSEN, RS .

NUMERISCHE MATHEMATIK, 1986, 48 (06) :671-697

[5] NUMERICAL INVERSION OF THE LAPLACE TRANSFORM - SURVEY AND COMPARISON OF METHODS [J].

DAVIES, B ;

MARTIN, B .

JOURNAL OF COMPUTATIONAL PHYSICS, 1979, 33 (01) :1-32

[6] ON THE NUMERICAL INVERSION OF THE LAPLACE TRANSFORM [J].

ESSAH, WA ;

DELVES, LM .

INVERSE PROBLEMS, 1988, 4 (03) :705-724

[7]

FRONTINI M, 1988, ALGORITHM APPROXIMAT

[8] GENERALIZED CROSS-VALIDATION AS A METHOD FOR CHOOSING A GOOD RIDGE PARAMETER [J].

GOLUB, GH ;

HEATH, M ;

WAHBA, G .

TECHNOMETRICS, 1979, 21 (02) :215-223

[9]

HANSEN C, 1988, INT SERIES NUMER MAT, V86, P179

[10]

Laurent P.-J., 1972, APPROXIMATION OPTIMI

← 1 2 →