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It is shown in this paper that, almost all current prevalent iterative\mbox{methods} for solving linear system of equations can be classified as whatwe called extended Krylov subspace methods. In this paper a new type ofiterative methods are introduced which do not depend on any Krylov subspaces.This type of methods are based on the so-called accumulated projectiontechnique proposed by authors. It overcomes some shortcomings of classicalRow-Projection technique and takes full advantages of the linear system.Comparing with traditional Krylov subspace methods which always depend on thematrix-vector multiplication with some fixed matrix, the newly introducedmethod (SAP) uses different projection matrices which differ in each step inthe iteration process to form an approximate solution. More importantly someparticular accelerative schemes (named as MSAP1 and MSAP2) are introduced toimprove the convergence of the SAP method. Numerical experiments show somesurprisingly improved convergence behavior; some superior experimental behaviorof MSAP methods over GMRES and block-Jacobi are demonstrated in somesituations.

A Stationary Accumulated Projection Method for Linear System of Equations