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Regularization by truncated Cholesky factorization: A comparison of four different approaches
- Source :
-
Journal of Complexity . Apr2007, Vol. 23 Issue 2, p225-244. 20p. - Publication Year :
- 2007
-
Abstract
- Abstract: Due to the principle of regularization by restricting the number of degrees of freedom, truncating the Cholesky factorization of a symmetric positive definite matrix can be expected to have a stabilizing effect. Based on this idea, we consider four different approaches for regularizing ill-posed linear operator equations. Convergence in the noise free case as well as—with an appropriate a priori truncation rule—in the situation of noisy data is analyzed. Moreover, we propose an a posteriori truncation rule and characterize its convergence. Numerical tests illustrate the theoretical results. Both analysis and computations suggest one of the four variants to be favorable to the others. [Copyright &y& Elsevier]
- Subjects :
- *FACTORIZATION
*LINEAR operators
*PARTIAL differential equations
*OPERATOR theory
Subjects
Details
- Language :
- English
- ISSN :
- 0885064X
- Volume :
- 23
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Complexity
- Publication Type :
- Academic Journal
- Accession number :
- 24782339
- Full Text :
- https://doi.org/10.1016/j.jco.2006.07.003