Solving Linear Equations Of Two Types Of Iterative Method And The Spectral Radius Of Matrix Hadamard Product Estimates

The high-performance solution of sparse linear algebra equations is very important in solving many problems from science and engineering applications, including computational fluid, numerical forecast of weather, and numerical simulation of nuclear blast.The traditional methods for solving the non-singular linear algebra equations Ax=b have both direct method and iterative method. The direct method based on matrix factorization, so it can not keep the sparse of the matrix. Compared with the direct method, the iterative method has a lot of advantages, for example, can keep the sparse of the matrix. For the iterative method, the selections of the iterative matrix have the decision function. The iterative matrix only selected by examinations the spectral radius of the matrix is less than 1 then can keep the iterative method to convergence. When the spectral radius of the iterative matrix is less than 1, smaller and more quick. In resolve the actual problems, sometimes although the spectral radius of the iterative matrix is less than 1, number with 1 close to very much, then convergent speed is very slow, it is ineffective. Need to adopt other ways at this time. To the primitive linear systems, the preconditioned technique is the valid method that resolves the convergent problem, become a heating problem. This paper mainly discusses one of the problems is to carry on precondition to the classic SOR and the AOR iterative methods. Another problem that this paper mainly discusses is the coefficient matrix of the linear system A is block tridiagonal matrix a kind of solution method of the linear algebra equations, Willian S. Helliwell put forward it (Pseudo Elimination) in 1977, the brief name was PE method. Through the calculation of the actual problems to express its convergence is quick, especially in the absolute values of the block off-diagonal entries of the coefficient A are smaller, its speed is more quick than other splitting methods.At the signal, picture processing and mathematics etc., a lot of problems can convert into the related calculation problems of the matrices Hadamard product, for example: separate a problem to the blind signal. Therefore, the research matrix Hadamard product has actual meaning and the theories meaning. The third problem that...