A modified landweber method for inverse problems
Author:
- 1 January 1999
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 20 (1-2) , 79-98
Abstract
Landweber's method is a well-known regularization method for linear and nonlinear ill-posed operator equations. We introduce a fast discrete version of this method. In combination with an a posteriori stopping rule we show that the modified Landweber method is a regularization method. Numerical examples for the linear and nonlinear case illustrate the efficiency of our method.Keywords
This publication has 19 references indexed in Scilit:
- Regularization of Inverse Problems1996
- A convergence analysis of the Landweber iteration for nonlinear ill-posed problemsNumerische Mathematik, 1995
- Factors influencing the ill-posedness of nonlinear problemsInverse Problems, 1994
- Convergence Rates for Maximum Entropy RegularizationSIAM Journal on Numerical Analysis, 1993
- Inverse Problems in the Mathematical Sciences1993
- Convergence rates for Tikhonov regularisation of non-linear ill-posed problemsInverse Problems, 1989
- A posteriori parameter choice for general regularization methods for solving linear ill-posed problemsApplied Numerical Mathematics, 1988
- Discrepancy principles for Tikhonov regularization of ill-posed problems leading to optimal convergence ratesJournal of Optimization Theory and Applications, 1987
- Optimal error bounds for cubic spline interpolationJournal of Approximation Theory, 1976
- An Iteration Formula for Fredholm Integral Equations of the First KindAmerican Journal of Mathematics, 1951