Regularization of linear ill-posed problems with noisy right hand side and noisy operator
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U. Tautenhahn
Abstract
For solving linear ill-posed problems regularization methods are required when the right hand side and the operator is with some noise. In the present paper regularized approximations are obtained by Tikhonov regularization, by regularized total least squares (RTLS) and by dual regularized total least squares (DRTLS). We discuss computational aspects and provide order optimal error bounds under two assumptions characterizing the smoothness of the unknown solution and the smoothing properties of the forward operator. The derived error bounds extend results from [S. Lu, S.V. Pereverzev, and U. Tautenhahn, Regularized total least squares: computational aspects and error bounds, Johann Radon Institute for Computational and Applied Mathematics, Report no. 2007-30, 2007.] where the above regularization methods are studied for finitely smoothing forward operators. We illustrate our theory by a special inverse heat conduction problem.
© de Gruyter 2008
Articles in the same Issue
- Simultaneous identification of independent parameters in elliptic equations — numerical studies
- Modulus of continuity of Nemytskii operators with application to the problem of option pricing
- Convergence rates and source conditions for Tikhonov regularization with sparsity constraints
- Metric and Bregman projections onto affine subspaces and their computation via sequential subspace optimization methods
- Regularization of linear ill-posed problems with noisy right hand side and noisy operator
- Chemnitz Symposium on Inverse Problems Chemnitz, Germany, September 27–28, 2007
Articles in the same Issue
- Simultaneous identification of independent parameters in elliptic equations — numerical studies
- Modulus of continuity of Nemytskii operators with application to the problem of option pricing
- Convergence rates and source conditions for Tikhonov regularization with sparsity constraints
- Metric and Bregman projections onto affine subspaces and their computation via sequential subspace optimization methods
- Regularization of linear ill-posed problems with noisy right hand side and noisy operator
- Chemnitz Symposium on Inverse Problems Chemnitz, Germany, September 27–28, 2007
