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- M. Y. Waziri, W. J. Leong
- 2010

Problem statement: The major weaknesses of Newton method for nonlinear equations entail computation of Jacobian matrix and solving systems of n linear equations in each of the iterations. Approach: In some extent function derivatives are quit costly and Jacobian is computationally expensive which requires evaluation (storage) of n×n matrix in every… (More)

- Mohammad Yusuf Waziri, Wah June Leong, Mustafa Mamat
- J. Applied Mathematics
- 2012

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)

- Wah June Leong, Malik Abu Hassan, Mohammad Yusuf Waziri
- Computers & Mathematics with Applications
- 2011

One of the widely used methods for solving a nonlinear system of equations is the quasi-Newton 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 quasi-Newton update. Application of quasi-Newton methods for large scale problems requires, in principle,… (More)

- M. Y. WAZIRI, M. MONSI
- 2010

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)

- Ibrahim Saidu, M. Y. Waziri, John Wiley, John R. Dorman, J. D. Lambert, Lawrence F. Shampine
- 2010

The derivation of fourth order Runge-Kutta method involves tedious computation of many unknowns and the detailed step by step derivation and analysis can hardly be found in many literatures. Due to the vital role played by the method in the field of computation and applied science/engineering, we simplify and further reduce the complexity of its derivation… (More)

- Mohammad Yusuf Waziri, Zanariah Abdul Majid
- Adv. Fuzzy Systems
- 2012

- Mohammad Yusuf Waziri, Zanariah Abdul Majid
- J. Applied Mathematics
- 2013

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)

- M. Y Waziri, W. J. Leong, M. A. Hassan, M. Monsi
- 2011 Fourth International Conference on Modeling…
- 2011

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)

- M. Y. Waziri, H. Aisha, A. I. Gambo
- 2011

In this paper, we compared and analyzed some newly diagonal variants of Newton methods for solving large-scale systems of nonlinear equations. Due to the fact that, the diagonal updating scheme is computationally less expensive than classical Newton methods and some of its variants. The two diagonal updating were introduced by Waziri et.al. [6] and Waziri… (More)

- Mohammad Yusuf Waziri, Zanariah Abdul Majid
- Int. J. Math. Mathematical Sciences
- 2013

Diagonal updating scheme is among the cheapest Newton-like methods for solving system of nonlinear equations. Nevertheless, the method has some shortcomings. In this paper, we proposed an improved matrix-free secant updating scheme via line search strategies, by using the steps of backtracking in the Armijo-type line search as a step length predictor and… (More)