Some First-Order-Like Methods for Solving Systems of Nonlinear Equations
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Author list: Aji, Sani; Kumam, Poom; Kumam, Wiyada
Publication year: 2023
Start page: 67
End page: 86
Number of pages: 20
ISBN: 9781000830842; 9781032318318
ISSN: 10269185
Languages: English-Great Britain (EN-GB)
Abstract
Finding the solution of nonlinear systems of equations is paramount due to their applications in many branches of science. For instance, they appear in signal and image recovery problems from compressed sensing, chemical equilibrium problems, among others. Some of the classical approaches for solving these systems include Newton and quasi-Newton methods which have fast convergence from reasonable initial points. However, these methods require solving Jacobian matrix or an approximation to it at every iteration, which affects their adequacy in solving large scale problems. In this chapter, we revisit some first order-like methods for solving these systems. These methods neither require the Jacobian information nor the storage of matrices, thus, suitable to handle large scale systems. We perform some numerical experiments and compare the performance of the methods to depicts their computational advantages. Moreover, under some assumptions, the global convergence of the methods is proved. © 2023 Taylor & Francis Group, LLC.
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