离散Newton型分裂方法的Kantorovich型定理  

The Kantorovich theorem of discrete Newton-type decomposition methods

作　　者：潘状元[1] 殷巧玉[2] 

机构地区：[1]哈尔滨理工大学应用科学学院,哈尔滨150080 [2]哈尔滨理工大学电气与电子工程学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2009年第5期576-584,共9页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(19971022)

摘　　要：对于牛顿型迭代格式等经典的算法,近年来经过很多学者的研究已经取得了丰硕的理论成果,包括收敛性定理、Kantorovich型定理和误差估计。局部收敛性定理需要假定了方程组有解,并且初始近似与解充分接近。然而对计算理论更为重要的是存在性、收敛性定理。在不知道解的情况下能够验证收敛条件,并且往往同时可以断定解的存在性乃至唯一性,因此对于各种迭代法建立存在性收敛性定理,始终是迭代法理论研究的中心课题之一。在Kantorovich型定理的条件下,给出了一种离散Newton型分裂方法的存在性及收敛性定理。Rich theoretical results of Newton-type iterative scheme and other classical algorithms have been made by many scholars in recent years, including convergence theorem, Kantorovich-type theorem and error estimate. The local convergence theorem requires the existence of solutions to nonlinear system of equations, and the initial ap- proximation approaches the solution sufficiently. But the existence and convergence theorem is more important to the theory of computation. The convergence conditions can be verified in the case that the solution is unknown, and assert simultaneously the existence and uniqueness of the solution. Therefore, establishing the existence and convergence theorems for kinds of the iteration methods has always been one of the centers of theoretical analysis in iteration method. The Kantorovich theorem for discrete Newton-type decomposition methods is given.

关 键 词：离散Newton型分裂法 存在性收敛性定理 非线性方程组 

分 类 号：O242.23[理学—计算数学]