An Effective Stationary Iterative Method Via Double Splittings Of Matrices

Many problems in scientific research will eventually be transformed into a large linear equation,such as the study of hydrodynamics,image processing and optimization problems and so on.Fast solution of large-scale linear equation with special structure is not only an important problem in numerical algebra research,but also its development promotes the developments of other disciplines.With the rapid improvement of computational ability,how to design a fast,robust and practical numerical solution according to the specific physical background and matrix properties has attracted extensive attentions of many mathematic researchers and mathematic enthusiasts.Through the unremitting efforts of teachers and engineers in the field of numerical algebra,the solution methods of the system are becoming more and more perfect,and the new algorithms which are more suitable for practical application are constantly updated and developed.In order to solve the linear system Ax=b,this paper constructs a new stable iteration algorithm called ADS iteration method by making two proper double splitting of coefficient matrix A of the equation.The convergence theorems and comparison theorems of the new iteration scheme are studied.In some specific cases,it is theoretically proved that the ADS method is superior to some existing double splitting methods.The numerical examples also validate the theoretical results,which show that our stable iteration algorithm is feasible and has superiority.