期刊
BIT NUMERICAL MATHEMATICS
卷 46, 期 3, 页码 589-606出版社
SPRINGER
DOI: 10.1007/s10543-006-0070-3
关键词
ill-posed problem; regularization; Lanczos tridiagonalization; Gauss quadrature; discrepancy principle
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.
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