Mohammad Yusuf Waziri

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We propose an approach to enhance the performance of a diagonal variant of secant method for solving large-scale systems of nonlinear equations. In this approach, we consider diagonal secant method using data from two preceding steps rather than a single step derived using weak secant equation to improve the updated approximate Jacobian in diagonal form.(More)
One of the widely used methods for solving a nonlinear system of equations is the quasiNewton method. The basic idea underlining this type of method is to approximate the solution of Newton’s equation by means of approximating the Jacobian matrix via quasiNewton update. Application of quasi-Newton methods for large scale problems requires, in principle,(More)
We propose a modification to Newton’s method for solving nonlinear equations, namely a Jacobian Computation-free Newton’s Method . Unlike the classical Newton’s method, the proposed modification neither requires to compute and store the Jacobian matrix, nor to solve a system of linear equations in each iteration. This is made possible by approximating the(More)
We present a new diagonal quasi-Newton update with an improved diagonal Jacobian approximation for solving large-scale systems of nonlinear equations. In this approach, the Jacobian approximation is derived based on the quasi-Cauchy condition. The anticipation has been to further improve the performance of diagonal updating, by modifying the quasi-Cauchy(More)
There is a great deal of interest on reducing overall computational budget of classical Newton’s method for solving nonlinear systems of equations. The appealing approach is based on chord Newton’s but the method mostly requires high number of iteration as the dimension of the systems increases. In this paper, we introduce a new procedure that will reduce(More)
This paper presents an improved diagonal Secant-like method using two-step approach for solving large scale systems of nonlinear equations. In this scheme, instead of using direct updating matrix in every iteration to construct the interpolation curves, we chose to use an implicit updating approach to obtain an enhanced approximation of the Jacobian matrix(More)
Abstract The basic requirement of Newtons method in solving systems of nonlinear equations is, the Jacobian must be non-singular. Violating this condition, i.e. the Jacobian to be singular the convergence is too slow and may even be lost. This condition restricts to some extent the application of Newton method. In this paper we suggest a new approach for(More)
We propose some improvements on a diagonal Newton's method for solving large-scale systems of nonlinear equations. In this approach, we use data from two preceding steps to improve the current approximate Jacobian in diagonal form. Via this approach, we can achieve a higher order of accuracy for Jacobian approximation when compares to other existing(More)