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An iterative Lavrentiev regularization method |
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| Authors: | S?Morigi |
| Institution: | (1) Dipartimento di Matematica, Universitá degli Studi di Bologna, Piazza Porta S. Donato 5, 40127 Bologna, Italy;(2) Department of Mathematical Sciences, Kent State University, Kent, 44242, OH, USA;(3) Dipartimento di Matematica CIRAM, Universitá degli Studi di Bologna, Via Saragozza 8, 40123 Bologna, Italy |
| Abstract: | This paper presents an iterative method for the computation of approximate solutions of large linear discrete ill-posed problems by Lavrentiev regularization. The method exploits the connection between Lanczos tridiagonalization and Gauss quadrature to determine inexpensively computable lower and upper bounds for certain functionals. This approach to bound functionals was first described in a paper by Dahlquist, Eisenstat, and Golub. A suitable value of the regularization parameter is determined by a modification of the discrepancy principle. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65R30, 65R32, 65F10 |
| Keywords: | ill-posed problem regularization Lanczos tridiagonalization Gauss quadrature discrepancy principle |
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