Approximation of Iteration Number for Gauss-Seidel Using Redlich-Kister Polynomial

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.

Enhancing the Color Set Partitioning in Hierarchical Tree (SPIHT) Algorithm Using Correlation Theory

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Redlich-Kister Finite Difference Solution for Solving Two-Point Boundary Value Problems by using Ksor Iteration Family

“…In addition to these functions, only one study has been explored to investigate the application of the Redlich-Kister approximation function in the numerical analysis particularly on constructing the mathematical model. For instance, in [25], the authors investigated the construction of two mathematical models based on the piecewise third-order Redlich-Kister polynomial model and the piecewise first-order polynomial model respectively to show the relationship of the number of iterations for Gauss-Seidel towards its corresponding grid size. The findings of their work concluded that the results of the piecewise third-order Redlich-Kister polynomial model gave highly accurate solutions as compared with the firstorder polynomial solution.…”