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An Inexact Newton Iterative Methods For Solving Large Sparse Nonlinear Equation Systems

Posted on:2010-01-08Degree:MasterType:Thesis
Country:ChinaCandidate:L L MengFull Text:PDF
GTID:2120360275996158Subject:Computational Mathematics
Abstract/Summary:PDF Full Text Request
The algorithm problem of solving nonlinear operator equation systems F(x)—0 in n dimensional spaces has been studing by many numerical scientists. Newton iteration method and its transmutations are the main algorithm for solving nonlinear equation. Now, the research for Newton equation solution becomes the hardcore of the Newton iterative method. Whether the nonlinear problems will be solved well or not is directly affected by the choice of the Newton equation solution. So it is very important meaningful to do the research of the Newton equation solution.The positive and skew-Hermitian splitting (PSS)method is an unconditionally convergent iterative method for solving large sparse positive definite systems of linear equations. By making use of the PSS iteration as the inner solver for the Newton method, we establish a class of Newton-PSS methods for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices at the solution points. For this class of inexact Newton methods, two types of local convergence theorems are proved under proper conditions. When we specialize the PS splitting to block-triangular(or trian-gular)and skew-Hermitian splitting(BTSS), (or TSS), the Newton-PSS methods naturally leads to a Newton-BTSS (or Newton-TSS) iteration method, which is a more practical and efficient the Newton-PSS methods. And numerical results are given to examine their feasibility and effectiveness, the advantages of the Newton-BTSS methods over the Newton-HSS methods show through solving systems of nonlinear equations arising from the finite difference discretization of a two-dimensional convection-diffusion equation perturbated by a nonlinear term.
Keywords/Search Tags:Systems of nonlinear equations, PSS iterative method, BTSS iterative method, Inexact Newton method, local convergence
PDF Full Text Request
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