An iterative method to compute minimum norm solutions of ill-posed problems in Hilbert spaces

We study an algorithm to compute minimum norm solution of ill-posed problems in Hilbert spaces and investigate its regularizing properties with discrepancy principle stopping rule. This algorithm results from straightly applying the LSQR method to the main problem before discretizing. In fact, the p...

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Veröffentlicht in:Afrika mathematica Jg. 30; H. 5-6; S. 797 - 816
Hauptverfasser: Jozi, Meisam, Karimi, Saeed, Salkuyeh, Davod Khojasteh
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2019
Springer Nature B.V
Schlagworte:
Algorithms
Applications of Mathematics
Hilbert space
History of Mathematical Sciences
Ill posed problems
Integral equations
Iterative methods
Mathematics
Mathematics and Statistics
Mathematics Education
Regularization
Regularization methods
Regularization method
45A05
Minimum norm
45P05
47B38
45Q05
First kind equations
45N05
47B34
Ill-posed problem
algorithm
ISSN:1012-9405, 2190-7668
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Zusammenfassung:We study an algorithm to compute minimum norm solution of ill-posed problems in Hilbert spaces and investigate its regularizing properties with discrepancy principle stopping rule. This algorithm results from straightly applying the LSQR method to the main problem before discretizing. In fact, the proposed algorithm obtains a sequence of approximate solutions of the original problem. In order to test the new algorithm, it is implemented to solve system of linear integral equations of the first kind and some examples are given. Moreover, we compare the presented algorithm with the Tikhonov regularization method to compute the least norm solution when there are more than one solution.
Bibliographie:ObjectType-Article-1
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ISSN:1012-9405
2190-7668
DOI:10.1007/s13370-019-00685-0