贯序和并行求解线性与非线性方程组的一类算法

A Class of Algorithms for Sequential and Parallel Solution of Algebraic Linear and Nonlinear Systems

1.引论 Abaffy,Broyden和spedicato在最近的论文中,提出了一类求解线性和非线性方程组的算法(有可能推广于求解其它问题,例如最优化问题).我们首先给出这类算法求解线性方程组时的基本形式.设线性方程组为 或把它写成矩阵形式 其中A=(a_1,…,a_m)是n×m阶矩阵,共秩q可以小于m.算法具有拟Newton型结构,其计算步骤如下:

In a series of papers Abaffy ,Broyden,Galantai and Spedicato have developed a class of algorithms for the solution in a finite number of steps of linear systems (full rank or not; underdetermined or determined; overdetermined in the least square sense) and of nonlinear systems (where they are a generalization of the Brown and Brent methods and possess local convergence properties at least comparable with those of Newton's method). The algorithms can be formulated in sequential and parallel versions.Preliminary numerical experiments indicate that some new algorithm for linear systems can be better than classical algorithms on ill conditioned problems.