S., Koh W and Jumat Sulaiman and Rasid Mail (2010) Quartersweep projected modified gaussseidel algorithm applied to linear complementarity problem. American Journal of Applied Sciences, 7 (6). pp. 790794. ISSN 15469239

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Abstract
Problem statement: Modified GaussSeidel (MGS) was developed in order to improve the convergence rate of classical iterative method in solving linear system. In solving linear system iteratively, it takes longer time when many computational points involved. It is known that by applying quartersweep iteration scheme, it can decrease the computational operations without altering the accuracy. In this study, we investigated the effectiveness of the new QuarterSweep Projected Modified GaussSeidel (QSPMGS) iterative method in solving a Linear Complementarity Problem (LCP). Approach: The LCP we looked into is the LCP arise in American option pricing problem. Actually, American option is a Partial Differential Complementarity Problem (PDCP). By using full, half and quartersweep CrankNicolson finite difference schemes, the problem was reduced to Linear Complementarity Problem (LCP). Results: Several numerical experiments were carried out to test the effectiveness of QSPMGS method in terms of number of iterations, computational time and root mean square error (RMSE). Comparisons were made with full, half and quartersweep algorithm based on Projected GaussSeidel (PGS) and Projected Modified GaussSeidel (PMGS) methods. Thus, the experimental results showed that the QSPMGS iterative method has the least number of iterations and shortest computational time. The RMSE of all tested methods are in good agreement. Conclusion: QSPMGS is the most effective among the tested iterative methods in solving LCP whereby it is fastest and the accuracy remains the same. Â© 2010 Science Publications.
Item Type:  Article 

Keyword:  CrankNicolson scheme, Linear complementarity problem, Projected modified gaussseidel, Quartersweep iteration 
Subjects:  Q Science > QA Mathematics > QA1939 Mathematics > QA101(145) Elementary mathematics. Arithmetic 
Department:  SCHOOL > School of Business and Economics SCHOOL > School of Science and Technology 
Depositing User:  ADMIN ADMIN 
Date Deposited:  04 Mar 2011 17:54 
Last Modified:  20 Oct 2017 14:54 
URI:  https://eprints.ums.edu.my/id/eprint/2042 
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