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An Incomplete Cholesky Factorization for Dense Symmetric Positive Definite Matrices

Authors
Journal
BIT Numerical Mathematics
0006-3835
Publisher
Springer-Verlag
Publication Date
Disciplines
  • Computer Science

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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