Approximation of iteration number for gauss-seidel using redlich-Kister polynomial

Mohammad Khatim Hasan, J. Sulaiman, S. Ahmad, M. Othman, S. A A Karim

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Problem statement: Development of mathematical models based on set of observed data plays a crucial role to describe and predict any phenomena in science, engineering and economics. Therefore, the main purpose of this study was to compare the efficiency of Arithmetic Mean (AM), Geometric Mean (GM) and Explicit Group (EG) iterative methods to solve system of linear equations via estimation of unknown parameters in linear models. Approach: The system of linear equations for linear models generated by using least square method based on (m+1) set of observed data for number of Gauss-Seidel iteration from various grid sizes. Actually there were two types of linear models considered such as piece-wise linear polynomial and piece-wise Redlich-Kister polynomial. All unknown parameters of these models estimated and calculated by using three proposed iterative methods. Results: Thorough several implementations of numerical experiments, the accuracy for formulations of two proposed models had shown that the use of the third-order Redlich-Kister polynomial has high accuracy compared to linear polynomial case. Conclusion: The efficiency of AM and GM iterative methods based on the Redlich-Kister polynomial is superior as compared to EG iterative method.

Original languageEnglish
Pages (from-to)956-962
Number of pages7
JournalAmerican Journal of Applied Sciences
Volume7
Issue number7
Publication statusPublished - 2010

Fingerprint

Gauss-Seidel
Iteration
Polynomial
Approximation
Linear Model
Geometric mean
System of Linear Equations
Unknown Parameters
Least Square Method
Piecewise Linear
High Accuracy
Numerical Experiment
Economics
Mathematical Model
Model-based
Grid
Engineering
Predict
Formulation
Model

Keywords

  • Arithmetic mean
  • Explicit group
  • Geometric mean
  • Poisson equation
  • Redlich-Kister model

ASJC Scopus subject areas

  • General

Cite this

Approximation of iteration number for gauss-seidel using redlich-Kister polynomial. / Hasan, Mohammad Khatim; Sulaiman, J.; Ahmad, S.; Othman, M.; Karim, S. A A.

In: American Journal of Applied Sciences, Vol. 7, No. 7, 2010, p. 956-962.

Research output: Contribution to journalArticle

Hasan, MK, Sulaiman, J, Ahmad, S, Othman, M & Karim, SAA 2010, 'Approximation of iteration number for gauss-seidel using redlich-Kister polynomial', American Journal of Applied Sciences, vol. 7, no. 7, pp. 956-962.
Hasan, Mohammad Khatim ; Sulaiman, J. ; Ahmad, S. ; Othman, M. ; Karim, S. A A. / Approximation of iteration number for gauss-seidel using redlich-Kister polynomial. In: American Journal of Applied Sciences. 2010 ; Vol. 7, No. 7. pp. 956-962.
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