The Pathological Step Length Based On Automatic Control System Of Linear Equations Algorithm Research

This paper mainly studies for the iteration with automatic step-size controlfor solving ill-conditioned linear equations; the solution of ordinary differentialequations in some classical iterative scheme is applied to solve ill-conditionedequations. The two new iterative improvements of solution are proposed on thebase of the automatic control step-size method proposed by Wu xinyuan. Theeffectiveness of the proposed algorithm is tested. And the two new iterativeimprovements are combined with principal component weighted pretreatmenttechnology. The numerical experiment results show that the iterative format ismore effective.In Chapter1, it introduces the related knowledge of ill-conditioned linearquations and its solution.In Chapter2, it introduces the basic idea of pretreatment, and somecommon pretreatment method.In Chapter3, on the base of the automatic control step-size methodproposed by Wu xin-yuan, the new iteration is claimed that the solution can beregarded that the explicit Euler formula is embedded with implicit Eulerformula for solving linear equations. The convergence of the iterative procedureis shown.The effectiveness of the proposed algorithm is tested.In Chapter4, it puts forward an automatic control step-size algorithm. Thenew iteration is claimed that the solution can be regarded that the Euler method is embedded with second-order R-K method for solving linear equations. Theconvergence of the iterative procedure is shown. The effectiveness of theproposed algorithm is tested.In Chapter5, it combines the Principal component weighted preconditioni-ng idea with the automatic control step-size formula. We propose the Principalcomponent weighted preconditioning embedded with the Euler formula and thePrincipal component weighted preconditioning embedded with the R-K formula.Through numerical experiments, we compare the experiment results with theexperiment results of the chapter3and the chapter4. The effectiveness of theproposed algorithm is tested.