A fast LDL-factorization approach for large sparse positive definite system and its application to one-to-one marketing optimization computation

LDL-factorization is an efficient way of solving Ax = b for a large symmetric positive definite sparse matrix A. This paper presents a new method that further improves the efficiency of LDL-factorization. It is based on the theory of elimination trees for the factorization factor. It breaks the computations involved in LDL-factorization down into two stages: 1) the pattern of nonzero entries of the factor is predicted, and 2) the numerical values of the nonzero entries of the factor are computed. The factor is stored using the form of an elimination tree so as to reduce memory usage and avoid unnecessary numerical operations. The calculation results for some typical numerical examples demonstrate that this method provides a significantly higher calculation efficiency for the one-to-one marketing optimization algorithm.

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