the authors obtained a new iterative method for solving linear sys-tems. This method can be considered as a projection method which uses a two-dimensional space at each step. In this paper，we generalize this method to athree-dimensional projection process. And a different approach is established,which is both theoretically and numerically proven to be better than（or at leastthe same as). In Chapter 2，firstly we illustrate Gauss-Seidel using projection steps，andgive further analysis for the new iterative method of in the Section 3 0fChapter 2. From the projection technique point of view，this method can beconsidered as a generalizing of Gauss-Seidel method which uses a two-dimensionalspace at each step. At the end of this chapter，we generalize this method to athree-dimensional projection process. As the theory in this chapter indicates，thenew iterative process gives better（or at least the same）reduction of the errorthan the iterative method proposed . In Chapter 3，the presented numerical examples show that，in most cases,the convergence rate of the new iterative process is better than（or at least thesame as）that of the iterative method proposed . Keywords: Projection technique;Linear system; Petrov-Galerkin（Galerkin）condition; Comparison results.
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