- Newton Method For Solving The Minimization Problem Block Relaxation

An iterative method for solving constraint and unconstraint extreme problem is studied in this paper. The main content is to use the iterative method to solve the minimization problem of nonlinear function, combining Block Jacobin-Newton Iterative Method and Block SOR-Newton Iterative Method which originated from Jacobin-Newton Iterative Method and SOR-Newton Iterative Method respectively. This paper contains three parts:Firstly, Jacobin-Newton Iterative Method, which takes linear function iterative method as basic iterative method and Newton iterative method as assisting iterative method, is introduced. Then unconstraint optimal extreme problem is solved based on this method. Especially when nonlinear function has particular form, the algorithm of Block Jacobin-Newton Iterative Method is achieved and its convergence is proved.Secondly, SOR-Newton Iterative Method, which takes nonlinear SOR iterative method as basic iterative method and Newton iterative method as assisting iterative method, is discussed. Compound Newton method, which originates from successive iterative method used to solve linear function and Newton method used to solve nonlinear function, is introduced to solve nonlinear unconstraint optimal problems and some constraint optimal problems. Then the algorithm and convergence of Block SOR-Newton Iterative Method is achieved.Finally, numerical calculation results, which use the Block Jacobin-Newton Iterative Method and Block SOR-Newton Iterative Method, are presented. The results prove that it is able to decrease computational complexity when computing the problem by blocks.