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Numerical Solution of Nonlinear Systems of Algebraic Equations
International Journal of Data Science and Analysis
Volume 4, Issue 1, February 2018, Pages: 20-23
Received: Jan. 29, 2018; Accepted: Feb. 27, 2018; Published: Mar. 23, 2018
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Authors
Kamoh Nathaniel Mahwash, Department of Mathematics and Statistics, Bingham University, Karu, Nigeria
Gyemang Dauda Gyang, Department of Mathematics and Statistics, Plateau State Polytechnic, Barkin Ladi, Nigeria
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Abstract
Considered in this paper are two basic methods of approximating the solutions of nonlinear systems of algebraic equations. The Steepest Descent method was presented as a way of obtaining good and sufficient initial guess (starting value) which is in turn used for the Broyden’s method. Broyden’s method on the other hand replaces the Newton’s method which requires the use of the inverse of the Jacobian matrix at every new step of iteration with a matrix whose inverse is directly determined at each step by up-dating the previous inverse. The result obtained by this method revealed that the setbacks encountered in computing the inverse of the Jacobian matrix at every step number is eliminated hence saving human effort and computer time. The obtained results also showed that the number of steps that is reduced when compared to Newton’s method used on the same problem.
Keywords
Convergent, Jacobian; Matrix, Approximation, Starting Value, Iteration, Nonlinear System
To cite this article
Kamoh Nathaniel Mahwash, Gyemang Dauda Gyang, Numerical Solution of Nonlinear Systems of Algebraic Equations, International Journal of Data Science and Analysis. Vol. 4, No. 1, 2018, pp. 20-23. doi: 10.11648/j.ijdsa.20180401.14
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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