NewtonType Decomposition Methods for Solving Nonlinear System of Equations 

Author  YinQiaoYu 
Tutor  PanZhuangYuan 
School  Harbin University of Science and Technology 
Course  Applied Mathematics 
Keywords  Newton secession law Convergence theorem of existence Nonlinear equations 
CLC  O242.23 
Type  Master's thesis 
Year  2008 
Downloads  137 
Quotes  0 
Classic algorithm of Newton  type iterative format in recent years , many scholars research has achieved fruitful results , including convergence theorem , Kantorovich type theorems and error estimates . Local convergence theorem presupposes equations solvable exist , and the initial approximate solution is sufficiently close to the iterative sequence converges to the solution of the equations . However, it is more important to calculate the theoretical existence, convergence theorem . Do not know the solution to verify the convergence conditions , and often at the same time can be concluded that the existence and even the only solution , therefore for various iterative method convergence theorem to establish the existence of , is always the center of one of the topics of the theoretical study of the iterative method . Newton type split method for solving nonlinear equations and discrete Newton split method , Jochen W.Schmidt, Wolfgang Hoyer and Christian Haufe only gives the local convergence theorem of Kantorovich type existence , and did not give the convergence theorem study split iterative schemes for solving nonlinear equations , given Kantorovich type convergence theorem of existence , the perfection of the system of the theory of nonlinear equations and therefore has important theoretical significance . This paper studies Newton splitting methods for solving nonlinear equations , given Kantorovich existence and convergence theorem . The paper is divided into four parts . The first chapter , in the introduction section mainly elaborated for solving nonlinear equations overview of the development at home and abroad , and describes the main contents of this article , subject , background and significance . Chapter II , Kantorovich type theorems for Newton splitting method . Chapter III gives the splitting methods for discrete Newton Kantorovich theorem . Chapter IV gives the Newton type semidiscrete splitting methods Kantorovich theorem . Perfect convergence theorem for Newton splitting methods .