Convergence Analysis of the Preconditioned Group Splitting Methods in Boundary Value Problems
Joint Authors
Mohammed Saeed, Abdulkafi
Mohd Ali, Norhashidah Hj.
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-09-11
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
The construction of a specific splitting-type preconditioner in block formulation applied to a class of group relaxation iterative methods derived from the centred and rotated (skewed) finite difference approximations has been shown to improve the convergence rates of these methods.
In this paper, we present some theoretical convergence analysis on this preconditioner specifically applied to the linear systems resulted from these group iterative schemes in solving an elliptic boundary value problem.
We will theoretically show the relationship between the spectral radiuses of the iteration matrices of the preconditioned methods which affects the rate of convergence of these methods.
We will also show that the spectral radius of the preconditioned matrices is smaller than that of their unpreconditioned counterparts if the relaxation parameter is in a certain optimum range.
Numerical experiments will also be presented to confirm the agreement between the theoretical and the experimental results.
American Psychological Association (APA)
Mohd Ali, Norhashidah Hj.& Mohammed Saeed, Abdulkafi. 2012. Convergence Analysis of the Preconditioned Group Splitting Methods in Boundary Value Problems. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-14.
https://search.emarefa.net/detail/BIM-504686
Modern Language Association (MLA)
Mohd Ali, Norhashidah Hj.& Mohammed Saeed, Abdulkafi. Convergence Analysis of the Preconditioned Group Splitting Methods in Boundary Value Problems. Abstract and Applied Analysis No. 2012 (2012), pp.1-14.
https://search.emarefa.net/detail/BIM-504686
American Medical Association (AMA)
Mohd Ali, Norhashidah Hj.& Mohammed Saeed, Abdulkafi. Convergence Analysis of the Preconditioned Group Splitting Methods in Boundary Value Problems. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-14.
https://search.emarefa.net/detail/BIM-504686
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-504686