A local convergence proof for the iterative aggregation method
نویسندگان
چکیده
منابع مشابه
A Convergence proof of an Iterative SubspaceMethod for Eigenvalues Problems ?
The generalized Davidson algorithm can be seen as a method which uses preconditioned residuals to create a subspace where it is easier to nd the smallest eigenvalue and its eigenvector. In this paper theoretical results proving convergence rates are shown. In addition, we investigate the use of multigrid as a preconditioner for this method and describe a new algorithm for calculating some other...
متن کاملEditionLocal convergence of the ( exact and inexact ) iterative aggregation method for linear systemsand Markov
The iterative aggregation method for the solution of linear systems is extended in several directions: to operators on Banach spaces; to the method with inexact correction, i.e., to methods where the (inner) linear system is in turn solved iteratively; and to the problem of nding stationary distributions of Markov operators. Local convergence is shown in all cases. Convergence results apply to ...
متن کاملA note on local and global convergence analysis of iterative aggregation-disaggregation methods
The purpose of the paper is to present some convergence properties of the iterative aggregation-disaggregation method for computing a stationary probability distribution vector of a column stochastic matrix. A sufficient condition for the local convergence property and the corresponding rate of convergence are established. Some global convergence considerations are presented. Several illustrati...
متن کاملConvergence Theorems for Two Iterative Methods A stationary iterative method for solving the linear system:
Recasting this in the form above we have 1 B M N − = − and . 1 c M b − = It is easy to show that this iteration is consistent for any splitting as long as M is nonsingular. Obviously, to be practical the matrix M must be selected so that the system My d = is easily solved. Popular choices for M are diagonal matrices (as in the Jacobi method), lower triangular matrices (as in the Gauss-Seidel an...
متن کاملOn the local convergence of a fifth-order iterative method in Banach spaces
A new predictor-corrector iterative procedure, that combines Newton’s method as predictor scheme and a fifth-order iterative method as a corrector, is designed for solving nonlinear equations in Banach spaces. We analyze the local order of convergence and the regions of accessibility of the new method comparing it with Newton’s method, both theoretical and numerically.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1983
ISSN: 0024-3795
DOI: 10.1016/0024-3795(83)90157-x