A Fast LDL-factorization Approach for Large Sparse Positive Definite System and Its Application to One-to-one Marketing Optimization Computation  

作　　者：Min Wu Bei He Jin-Hua She 

机构地区：[1]School of Information Science and Engineering, Central South University, Changsha 410083, PRC [2]School of Bionics, Tokyo University of Technology, Tokyo 192-0982,Japan

出　　处：《International Journal of Automation and computing》2007年第1期88-94,共7页国际自动化与计算杂志（英文版）

基　　金：This work was supported in part by the National Natural Science Foundation of PRC (No.60425310);the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE,PRC.

摘　　要：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.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.

关 键 词：Sparse matrix factorization elimination tree structure prediction one-to-one marketing optimization. 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]