三类新的求解广义最小二乘问题的预处理GAOR方法  

THREE NEW PRECONDITIONED GENERALIZED AOR METHODS FOR SLOVING GENERALIZED LEAST-SQUARES PROBLEMS

作　　者：王丽 Wang Li(College of Mathematics and Statistics,Northwest Normal University,LanZhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《数值计算与计算机应用》2020年第4期282-296,共15页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11861059),西北师范大学计算数学创新团队(NWNU-LKQN-17-5)资助.

摘　　要：本文提出了用以加速求解广义最小二乘问题的2×2块线性系统的GAOR方法的三类新的预处理子,研究了新预处理GAOR方法的比较定理.所得的比较结果表明当原GAOR方法收敛时,我们提出的新预处理GAOR迭代方法的收敛速度优于原GAOR.最后,给出的数值算例也很好的验证了新预处理方法的有效性.In this paper,we propose three kinds of new preconditioners of the GAOR method,which for accelerated solving a class of block 2×2 linear systems arising from the generalized leastsquares problems.The comparison theorems of the new preconditioned GAOR methods are studied.Comparison results indicate that the convergence rates of the new preconditioned GAOR iterative methods are better than those of the original GAOR methods whenever the original GAOR method is convergent.Finally,a numerical example is given to demonstrate the effectiveness of the new preconditioned GAOR methods.

关 键 词：广义最小二乘问题 预处理子 GAOR方法 收敛性 比较定理 

分 类 号：O241.6[理学—计算数学]