Chebyshev Polynomial Acceleration Of Different SOR Iterative Method

Many scientific computing problems eventually turn into a linear system to solve the problems. And linear least squares problems [26] is a important areas in mathematical calculation, also is a very active research field. It is applied to many scientific computing areas such as geodesy, photogrammetry, structural analysis, and structural molecular.Following the classic method such as: Jacobi, GS, SOR, SSOR methods, people put forward their block iterative methods such as: BJ method, BGS method, BSOR method, SBSOR method, AOR ([10], [39], [41])method, GSOR method [42], SOR-like approach ([23], [24], [27]), AGSOR method [15], etc. Splitting iterative method is very effective to solve linear least squares problems, but for morbid equation, a number of iterative methods have their deficient. In the iterative method, the convergence and convergence rate play a major role. Below we shall accelerate some different iterative methods. Through the discussions of the convergence of accelerated iterative matrix, we prove that our method is superior to the iterative method before, and is efficient for sick equations.In this paper, we apply the Chebyshev polynomials to the different SOR iterations, and present three new iterative format to solve linear least squares problems. Through discussing of the convergence, and comparing with the iteration method before and the extrapolation method, we found that the new method is superior to the method before. And the corresponding optimal convergence rate is twice the extrapolation method. Finally, we compare the two new methods and give numerical examples.