A Novel Parallel Algorithm Based on the Gram-Schmidt Method for Tridiagonal Linear Systems of Equations
Joint Authors
Ghodsi, Seyed Roholah
Taeibi-Rahni, Mohammad
Source
Mathematical Problems in Engineering
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-01-13
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
This paper introduces a new parallel algorithm based on the Gram-Schmidt orthogonalization method.
This parallel algorithm can find almost exact solutions of tridiagonal linear systems of equations in an efficient way.
The system of equations is partitioned proportional to number of processors, and each partition is solved by a processor with a minimum request from the other partitions' data.
The considerable reduction in data communication between processors causes interesting speedup.
The relationships between partitions approximately disappear if some columns are switched.
Hence, the speed of computation increases, and the computational cost decreases.
Consequently, obtained results show that the suggested algorithm is considerably scalable.
In addition, this method of partitioning can significantly decrease the computational cost on a single processor and make it possible to solve greater systems of equations.
To evaluate the performance of the parallel algorithm, speedup and efficiency are presented.
The results reveal that the proposed algorithm is practical and efficient.
American Psychological Association (APA)
Ghodsi, Seyed Roholah& Taeibi-Rahni, Mohammad. 2011. A Novel Parallel Algorithm Based on the Gram-Schmidt Method for Tridiagonal Linear Systems of Equations. Mathematical Problems in Engineering،Vol. 2010, no. 2010, pp.1-17.
https://search.emarefa.net/detail/BIM-458892
Modern Language Association (MLA)
Ghodsi, Seyed Roholah& Taeibi-Rahni, Mohammad. A Novel Parallel Algorithm Based on the Gram-Schmidt Method for Tridiagonal Linear Systems of Equations. Mathematical Problems in Engineering No. 2010 (2010), pp.1-17.
https://search.emarefa.net/detail/BIM-458892
American Medical Association (AMA)
Ghodsi, Seyed Roholah& Taeibi-Rahni, Mohammad. A Novel Parallel Algorithm Based on the Gram-Schmidt Method for Tridiagonal Linear Systems of Equations. Mathematical Problems in Engineering. 2011. Vol. 2010, no. 2010, pp.1-17.
https://search.emarefa.net/detail/BIM-458892
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-458892