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On Newton-Triangle Splitting Methods For The Systems Of Nonlinear Equations And Its Modification

Posted on:2015-04-19Degree:MasterType:Thesis
Country:ChinaCandidate:J Y HuFull Text:PDF
GTID:2180330434458485Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
Large sparse systems of nonlinear equations arise in many areas of scientific com-puting and engineering applications, for example, in discretizations of nonlinear differ-ential and integral equations, numerical optimization and so on. So, looking for a quick and efficient method in solving nonlinear equations is particularly important.Firstly, by making use of the Triangle Splitting iteration Method of non-Hermitian positive definite matrices as the inner solver of inexact Newton method, a class of inexact Newton-Triangle Splitting iteration method for solving large sparse system of nonlinear equations with positive definite Jacobian matrices is established in the paper. The local convergence theorems and semilocal convergence theorem are proved under proper conditions. The numerical results are given to examine the feasibility and effectivity of inexact Newton-Triangle Splitting iteration method.Secondly, a new modified Newton-Triangle Splitting iteration method is proposed based on Newton-Triangle Splitting iteration method. The local convergence theorem and semilocal convergence theorem are proved under the same conditions. Finally, numerical example is given to compare Newton-Triangle Splitting iteration method with the new modified Newton-Triangle Splitting iteration method, which shows that the new modified Newton-Triangle Splitting iteration method spends less CPU time and the numbers of the outer iteration steps.
Keywords/Search Tags:Large sparse systems, Nonlinear equations, The Triangle Split-ting Method, Inexact Newton method, Local convergence, Semilocal Local convergence
PDF Full Text Request
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