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
S. Morigi, F. Sgallari, L.Reichel (2006). An Iterative Lavrentiev regularization method. BIT, 46(3), 589-606 [10.1007/s10543-006-0070-3].
An Iterative Lavrentiev regularization method
MORIGI, SERENA;SGALLARI, FIORELLA;
2006
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 principleI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
