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Sufficient and Necessary Conditions of the Convergence of AOR and 2PPJ Iterative Methods for a Special Class of Matrices

Author: GaoShuLing
Tutor: ChangDaWei
School: Shaanxi Normal University
Course: Computational Mathematics
Keywords: Extrapolation iterative matrix AOR iterative method 2PPJ iterative method Convergence The necessary and sufficient conditions
CLC: O241.6
Type: Master's thesis
Year: 2010
Downloads: 30
Quote: 0
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Algorithm for solving a large sparse matrix linear equations, has been the value of the workers in the study. Iterative rule of thumb is to solve an important method for this type of Linear Equations. Iterative scheme convergence and convergence rate is becoming address the core of the various types of linear equations. iterative format choices directly affect the result of good or bad of a variety of linear equations, especially in recent years, is to become the focus of many people, which can be seen, the iteration unusual scientific value and practical significance of the Study. general, the iterative convergence of the nature of the coefficient matrix is ??closely related to the M array consistently ordered array. different matrix iterative method is not the same. discuss an iterative, usually based on a certain type of matrix premise. consistently ordered matrix and consistently ordered vector since the fifth chapter of the book of the Young \has been a lot of discussion in the literature on the group AOR method of convergence, but the results are mostly fully non-necessary conditions of convergence. scholars matrix A (1,1), respectively, for the coefficients of the linear equations consistently ordered array and Jacobi Matrix eigenvalues ??are all real numbers or all pure imaginary or zero conditions to discuss the convergence of the AOR range, gives a necessary and sufficient condition for such equations AOR iterative convergence. text Part 3 major to discuss the convergence of two common iteration AOR Iterative 2PPJ of iterations. summarizes the conditions of the convergence of two iterative methods and seek convergence of two iterative methods. extrapolation iteration in Chapter 1 of this paper and some basic knowledge of linear equations, the part to pave the way for the second three chapters. Chapter 2 of this article focuses on when the coefficient matrix of linear equations A (1,1) consistently ordered matrix and the eigenvalues ??of the Jacobi matrix equal to the modulus of the real part and the imaginary part of the mold plural AOR iterative convergence range problem. gives a necessary and sufficient condition for such equations AOR iterative convergence discussed in Chapter 3 of this paper when linear The convergence range of 2PPJ iterative equations AX = 6 coefficients of the Jacobi matrix of the matrix A is equal to the modulus of the eigenvalues ??of the real and imaginary parts. come to such linear equations a necessary and sufficient condition for 2PPJ iterative convergence. Some numerical example is given to this result be explained.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > Linear algebra method of calculating
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