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Semiconvergence of extrapolated iterative methods for singular linear systems

✍ Scribed by Yongzhong Song

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
89 KB
Volume
106
Category
Article
ISSN
0377-0427

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✦ Synopsis

In this paper, we discuss convergence of the extrapolated iterative methods for solving singular linear systems. A general principle of extrapolation is presented. The semiconvergence of an extrapolated method induced by a regular splitting and a nonnegative splitting is proved whenever the coe cient matrix A is a singular M -matrix with 'property c' and an irreducible singular M -matrix, respectively. Since the (generalized, block) JOR and AOR methods are respectively the extrapolated methods of the (generalized, block) Jacobi and SOR methods, so the semiconvergence of the (generalized, block) JOR and AOR methods for solving general singular systems are proved. Furthermore, the semiconvergence of the extrapolated power method, the (block) JOR, AOR and SOR methods for solving Markov chains are discussed.

πŸ“œ SIMILAR VOLUMES

On the convergence of general stationary
On the convergence of general stationary iterative methods for range-Hermitian singular linear systems
✍ Naimin Zhang; Yi-Min Wei πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 142 KB πŸ‘ 1 views

## Abstract General stationary iterative methods with a singular matrix __M__ for solving range‐Hermitian singular linear systems are presented, some convergence conditions and the representation of the solution are also given. It can be verified that the general Ortega–Plemmons theorem and Keller