相容线性系统的行投影块迭代算法  

Block-Iterative Algorithm with Row Projection for Consistent Linear System

作　　者：张燕[1] 杨洋[1] 陆伟东[1] 

机构地区：[1]南京审计学院应用数学系

出　　处：《南京师范大学学报（工程技术版）》2006年第1期47-51,66,共6页Journal of Nanjing Normal University(Engineering and Technology Edition)

基　　金：南京审计学院青年科研基金资助项目(NSK2005/C08)

摘　　要：探讨了一种行投影块迭代算法来求解大型相容线性系统.该算法基于Kaczmarz算法,主要思想是首先对系数矩阵A进行分块,然后通过选取离当前迭代点距离最远的块来进行投影,并将投影作为下一个迭代点.数值结果显示,行投影迭代算法对坏条件问题非常有效,所提出的算法与经典的C imm ino算法相比,收敛速度更快.另外还提出一种新的对系数矩阵A分块的列分解策略,该策略基于每块的列相关性估计而得出.In this paper we discuss a block-iterative algorithm with row projection for solving large consistent linear system. This algorithm is based on the Kaczmarz algorithm. The key idea is that the coefficient matrix A is firstly divided into blocks, then the current iterative point is projected onto the remotest block measured by the distance between the iterative point and the block, and the projection is taken as the next iterative point. Numerical simulations show that block-iterative algorithm with row projection is very efficient for solving ill-conditioned problems. Compared with the classical Cimmino algorithm, algorithm accelerates the convergence greatly. In addition we present a new column partition strategy, based on the estimate of column-dependence of each block, to divide the coefficient matrix A.

关 键 词：行投影块迭代算法 列分解策略 最远块 

分 类 号：O29[理学—应用数学]