Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4628153 | Applied Mathematics and Computation | 2014 | 8 Pages |
Abstract
In this paper we consider the Lavrentiev regularization method and a modified Newton method for obtaining stable approximate solution to nonlinear ill-posed operator equations F(x)=y where F:D(F)âXâ¶X is a nonlinear monotone operator or Fâ²(x0) is nonnegative selfadjoint operator defined on a real Hilbert space X. We assume that only a noisy data yδâX with ây-yδâ⩽δ are available. Further we assume that Fréchet derivative Fâ² of F satisfies center-type Lipschitz condition. A priori choice of regularization parameter is presented. We proved that under a general source condition on x0-xË, the error âxË-xn,αδâ between the regularized approximation xn,αδ(x0,αδâx0) and the solution xË is of optimal order. In the concluding section the algorithm is applied to numerical solution of the inverse gravimetry problem.
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Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Vladmir Vasin, Santhosh George,