An Incomplete Cholesky Factorization for Dense Symmetric Positive Definite Matrices |
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| Authors: | Chih-Jen Lin Romesh Saigal |
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| Institution: | (1) Department of Computer Science and Information Engineering, National Taiwan University, Taipei, 106, Taiwan.;(2) Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, 48109, USA. |
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| Abstract: | In this paper, we study the use of an incomplete Cholesky factorization (ICF) as a preconditioner for solving dense symmetric positive definite linear systems. This method is suitable for situations where matrices cannot be explicitly stored but each column can be easily computed. Analysis and implementation of this preconditioner are discussed. We test the proposed ICF on randomly generated systems and large matrices from two practical applications: semidefinite programming and support vector machines. Numerical comparison with the diagonal preconditioner is also presented. |
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| Keywords: | Incomplete Cholesky factorization conjugate gradient methods dense linear systems |
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