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Application of Modified Cramer’s Rule in Quadrant Interlocking Factorization


Affiliations
1 Department of Mathematical Sciences, Federal University Lokoja, 1154 Lokoja, Kogi State, Nigeria
2 School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Pulau Pinang, Penang, Malaysia
 

Objectives: To show that modified Cramer’s rule is better than classical Cramer’s rule for solving linear systems in quadrant interlocking factorization or WZ factorization. Methods: The relative residual measurement of modified Cramer’s rule was compared with classical Cramer’s rule. Furthermore, we apply the rules in WZ factorization and evaluate their matrix norm on AMD and Intel processor. Findings: This study shows that the residual measurements of modified Cramer’s rule are 20% better than Cramer's rule. It also shows that the matrix norm of Cramer’s rule in WZ factorization is higher than using modified Cramer’s rule in the factorization. Application/improvements: Modified Cramer’s rule can be used to solve simple linear system. Applying the modified Cramer’s rule in WZ factorization using parallel computer or shared memory multiprocessor networks such as Intel Xeon Phi, Sunway Taihulight or OLCF-4 should be strongly considered.
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  • Application of Modified Cramer’s Rule in Quadrant Interlocking Factorization

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Authors

Olayiwola Babarinsa
Department of Mathematical Sciences, Federal University Lokoja, 1154 Lokoja, Kogi State, Nigeria
Hailiza Kamarulhaili
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Pulau Pinang, Penang, Malaysia

Abstract


Objectives: To show that modified Cramer’s rule is better than classical Cramer’s rule for solving linear systems in quadrant interlocking factorization or WZ factorization. Methods: The relative residual measurement of modified Cramer’s rule was compared with classical Cramer’s rule. Furthermore, we apply the rules in WZ factorization and evaluate their matrix norm on AMD and Intel processor. Findings: This study shows that the residual measurements of modified Cramer’s rule are 20% better than Cramer's rule. It also shows that the matrix norm of Cramer’s rule in WZ factorization is higher than using modified Cramer’s rule in the factorization. Application/improvements: Modified Cramer’s rule can be used to solve simple linear system. Applying the modified Cramer’s rule in WZ factorization using parallel computer or shared memory multiprocessor networks such as Intel Xeon Phi, Sunway Taihulight or OLCF-4 should be strongly considered.

References