ABS投影算法的两个改进

本文将求解线性方程的ABS投影算法进行两方面的改进和推广，一是使算法在第K次迭代产生的点xk＋1不仅满足前k个方程，还尽可能地使得在点xk处成立的方程j（j＞k）在xk＋1处仍成立，称之为强ABS投影算法，另外初始选代矩阵由非奇异的减弱为任意的．二是建立了系数矩阵有零子块的方程组的ABS投影算法，其存贮量和计算量比原ABS投影算法小．ABS算法可以作为这两种改进算法的特别情形．

TWO IMPROVEMENTS FOR ABS PRJECTION METHOD

Two improvements and popularizations of ABS projection method for linear equations are studiedin this paper. The one is to make the interation point xk+1satisfies not only the preceding k equations,but alsothe equationj(j>k)at which point xk already holded, so it is called strong ABS projection method; moreover,it weakens the condition for initial interation matrix such that it may be singular. The others is to present aimprove ABS projection method for equations whose coefficent matrix contains zero submatrices,its amountof compution and stock is smaller than the ABS projection method. ABS method may be considered to be aspecial case of the two modified methods.