The Study Of CRI-based Iteration Method For Solving Systems Of Linear And Nonlinear Equations

Concentrating on the problems of linear and weakly nonlinear equations in complex field,which widely appear in the field of scientific calculation and engineering application,this paper presents several new methods based on CRI method to solve these problems.The main content of the research is divided into two parts.First of all,the modified CRI(MCRI)method in the general case is introduced in this paper,using the block form successive over relaxation(SOR)iterative technique.Simultaneously,based on the minimal residual method and the two-parameter technique,this paper proposes the Minimum Residual CRI(MRCRI)method.Furthermore,in terms of theoretical analysis,it is verified that both new methods are convergent under suitable conditions.Numerical experimental results present that the two new methods perform outstandingly in solving systems of linear equations.When compared with other methods,such as CRI,PMHSS and GSOR,the resolution efficiency of the two new methods has been greatly improved,and the MRCRI method demonstrates robustness.Secondly,this paper follows the Picard iterative method for solving systems of weakly nonlinear equations,and takes the MCRI method as its internal iterative method to construct the Picard MCRI(P-MCRI)method with a double iteration form.Simultaneously,a nonlinear MCRI-like(NL-MCRI)method that avoids explicitly calling the internal iterative method is also derived.In addition,in view of the difference in the number of fixed point equations between the CRI method and the MCRI method,a nonlinear CRI-like(NL-CRI)method is separately proposed in this paper.Subsequently,using the analysis of the improved generalized Ostrowski theorem,the local convergence properties of the three new methods are proved.The results of the numerical experiments verify the effectiveness of the P-MCRI method,the NL-MCRI method and the NL-CRI method in solving the system of weakly nonlinear equations under two specific parameters.Moreover,the performance of the Picard MCRI method is not weaker than that of the Picard PGSOR method with a single parameter,and is better than that of the Picard AGSOR method with a single parameter.Finally,through analyzing the results of parameter sensitivity experiment,the different characteristics of P-MCRI method under two specific parameters are obtained in this paper.