New parallel algorithms for direct solution of sparse linear systems: Part I - Symmetric coefficient matrix

作     者：Gopalan, K Murthy, CSR 

作者机构：SUNY Stony Brook Dept Comp Sci Stony Brook NY 11794 USA Indian Inst Technol Dept Comp Sci & Engn Madras 600036 Tamil Nadu India 

出 版 物：《INTERNATIONAL JOURNAL OF HIGH SPEED COMPUTING》 (国际高速计算杂志)

年 卷 期：1997年第9卷第4期

页      面：259-290页

核心收录：

学科分类：08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：linear equation sparse symmetric system Cholesky factorization parallel algorithm bidirectional scheme multiprocessor 

摘      要：In this paper, we propose a new parallel bidirectional algorithm, based on Cholesky factorization, for the solution of sparse symmetric system of linear equations. Unlike the existing algorithms, the numerical factorization phase of our algorithm is carried out in such a manner that the entire back substitution component of the substitution phase is replaced by a single step division. Since there is a substantial reduction in the time taken by the repeated execution of the substitution phase, our algorithm is particularly suited for the solution of systems with multiple b-vectors. The effectiveness of our algorithm is demonstrated by comparing it with the existing parallel algorithm, based on Cholesky factorization, using extensive simulation studies on two-dimensional problems discretized by FEM.