一般限制线性方程组的迭代解法

ITERATIVE SOLUTION OF GENERAL RESTRICTED LINEAR EQUATIONS

本文研究带限制条件的线性方程组Ａｘ＝ｂ，Ｘ∈Ｔ的选代解法，这里Ａ∈Ｃｍ×ｎ，ｂ∈Ｃｍ，Ｔ是Ｃｎ的子空间．我们构造了迭代格式ｘｏ＝０，ｒｋ＝ｂ—Ａｘｋ，ｘｋ＋１＝ｘｋ＋βＹｒｋ，ｋ＝０，１，…其中β是非零实参数，Ｙ是参矩阵；在方程组有解时，给出了参数β与参阵Ｙ的选取方法，以保证选代序列｛ｘｋ｝收敛到它的一个解．

in this paper we study iterative methods for solving the general restricted linearequations Ax=b,x∈T, where A ∈ Cm×n,b ∈ Cm and T is a subspace of Cn.Weconstruct the iterative schemexo =0,Tk=b-Axk,Xk+1 = Xk + βYrk,k = 0,1,… ,where 0≠βis a real parameter and Y is a parameter matrix. In the case where theequations above has a solution, we give a choice of β and Y such that the iterative sequence{xk}converges to its solution.