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Park, C.H. and Shim, H.T. (2005) What Is the Homotopy Method for a System of Nonlinear Equations (Survey)? Journal of Applied Mathematics and Computing, 17, 689-700.

has been cited by the following article:

• TITLE: Multistep Quadrature Based Methods for Nonlinear System of Equations with Singular Jacobian

  AUTHORS: Oghovese Ogbereyivwe, Kingsley Obiajulu Muka

  KEYWORDS: Nonlinear System of Equations, Quadrature Formula, Singular Jacobian, Mul-tistep Iterative Methods

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.7 No.3, March 28, 2019

  ABSTRACT: Methods for the approximation of solution of nonlinear system of equations often fail when the Jacobians of the systems are singular at iteration points. In this paper, multi-step families of quadrature based iterative methods for approximating the solution of nonlinear system of equations with singular Jacobian are developed using decomposition technique. The methods proposed in this study are of convergence order , and require only the evaluation of first-order Frechet derivative per iteration. The approximate solutions generated by the proposed iterative methods in this paper compared with some existing contemporary methods in literature, show that methods developed herein are efficient and adequate in approximating the solution of nonlinear system of equations whose Jacobians are singular and non-singular at iteration points.