求解大型矩阵特征值问题的并行块Davidson方法  

Parallel Block Davidson Method for Solving Large Scale Eigenvalue Problem

作　　者：王顺绪[1] 戴华[1] 

机构地区：[1]南京航空航天大学理学院

出　　处：《南京航空航天大学学报》2007年第6期814-818,共5页Journal of Nanjing University of Aeronautics & Astronautics

摘　　要：针对拥有共享内存的并行计算环境和微机网络并行计算环境,给出了求解大型稀疏对称矩阵部分极端特征对的并行块Davidson方法。该方法将矩阵A按行块分配到各处理器上,各处理器利用矩阵A的行块和投影子空间的正交基所组成矩阵V的行块进行运算,减少了处理机之间的通讯次数,实现了算法的并行计算。在微机网络并行计算环境和拥有共享内存并行计算环境IBMP650上的数值试验表明,该算法非常有效。A parallel block Davidson method is presented for solving extreme eigenpairs of large sparse symmetric matrix based on PC network parallel environment and shared memory parallel environment. The row blocks of matrix A are distributed on each processor. The individual processors run under the control of the program based on the orthogonal basis of projection subspace V and the row block of matrix A. So less information is exchanged among processors. Numerical experiments in the PC network parallel environment and the shared memory environment IBMP650 show that the algorithm is effective.

关 键 词：对称矩阵 特征值问题 Davidson方法 并行块Davidson方法 

分 类 号：O241[理学—计算数学]