Newton-Type Decomposition Methods for Solving Nonlinear System of Equations
|School||Harbin University of Science and Technology|
|Keywords||Newton -secession law Convergence theorem of existence Nonlinear equations|
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 semi-discrete splitting methods Kantorovich theorem . Perfect convergence theorem for Newton splitting methods .