Regularization by truncated Cholesky factorization: A comparison of four different approaches

Authors:
Barbara Kaltenbacher
Affiliations:
University of Erlangen, Germany
Venue:
Journal of Complexity
Year:
2007

Citing 2
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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.