The backus-gilbert method revisited: background, implementation and examples
- 1 January 1987
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 9 (9-10) , 917-943
- https://doi.org/10.1080/01630568708816267
Abstract
The paper deals with the Backus-Gilbert or averaging kernel inversion of linear integral equations. The theoretical background of the method is developed: it is shown that the method leads to a sequence of linear pointwise estimates, which are asymptotically unbiased when no error is present. Anumerical implementation is given. Finally, the algorithm is applied to numerical differentiation, Laplace transform inversion and to a geophysical inverseproblem arising in electromagnetic sounding.Keywords
This publication has 4 references indexed in Scilit:
- Numerical inversion of the Laplace transform by the use of Pollaczek polynomialsZeitschrift für angewandte Mathematik und Physik, 1984
- Pitfalls in the Numerical Solution of Linear Ill-Posed ProblemsSIAM Journal on Scientific and Statistical Computing, 1983
- Least squares with a quadratic constraintNumerische Mathematik, 1980
- Algorithms for the regularization of ill-conditioned least squares problemsBIT Numerical Mathematics, 1977