On the Picard-Mann approach for hybridizing the double direction method for solving a system of nonlinear equations.

Subject Areas : Non linear Programming

Abubakar Halilu ¹ , Aliyu kiri ² , Mohammed Waziri ³

1 - Sule Lamido University, Kafin Hausa
2 - Department of Mathematics, Bayero University, Kano
3 - Department of Mathematics, Bayero University, Kano

Received: 2021-12-15 Accepted : 2022-07-06 Published : 2022-03-01

Keywords:

References:

Abdullahi, H., Halilu, A. S., & Waziri, M. Y. (2018). A modified conjugate gradient method via a double direction approach for solving large-scale symmetric nonlinear systems. Journal of Numerical Mathematics and Stochastics, 10(1), 32-44.

Dennis Jr, J. E., & Schnabel, R. B. (1983). Numerical methods for unconstrained optimization and nonlinear equations prentice-hall series in computation. Mathematics, Englewood Cliffs, NJ.

Dolan, E. D., & Moré, J. J. (2002). Benchmarking optimization software with performance profiles. Mathematical programming, 91(2), 201-213.

Halilu A.S. and Waziri M.Y.: Enhanced matrix-free method via double step length approach for solving systems of nonlinear equations. Int J app Math Res. 2017; 6:147–156 .

Halilu, A. S., & Waziri, M. Y. (2017). A transformed double step length method for solving large-scale systems of nonlinear equations. Journal of Numerical Mathematics and Stochastics, 9(1), 20-23.

Halilu, A. S., & Waziri, M. Y. (2018). An improved derivative-free method via double direction approach for solving systems of nonlinear equations. Journal of the Ramanujan Mathematical Society, 33(1), 75-89.

Halilu, A. S., & Waziri, M. Y. (2020). Solving systems of nonlinear equations using improved double direction method. Journal of the Nigerian Mathematical Society, 39(2), 287-301.

Halilu, A. S., Waziri, M. Y., & Musa, Y. B. (2020). Inexact double step length method for solving systems of nonlinear equations. Statistics, Optimization & Information Computing, 8(1), 165-174.

Khan, S. H. (2013). A Picard-Mann hybrid iterative process. Fixed Point Theory and Applications, 2013(1), 1-10.

Li, D., & Fukushima, M. (1999). A globally and superlinearly convergent gauss--Newton-based BFGS method for symmetric nonlinear equations. SIAM Journal on numerical Analysis, 37(1), 152-172.

Petrović, M. J. (2015). An accelerated double step size model in unconstrained optimization. Applied Mathematics and Computation, 250, 309-319.

Petrović, M. J., & Stanimirović, P. S. (2014). Accelerated double direction method for solving unconstrained optimization problems. Mathematical Problems in Engineering, 2014.

Petrovic´, M.J., Stanimirovic´, P.S., Kontrec, N., Mladenovic´, J. Hybrid Modification of accelerated double direction method. Math. Probl. Eng. 2018; Article D 1523267: 8 pages. doi.org/10.1155/2018/1523267.

Yuan, G., & Lu, X. (2008). A new backtracking inexact BFGS method for symmetric nonlinear equations. Computers & Mathematics with Applications, 55(1), 116-129.

Yusuf, M. W., June, L. W., & Hassan, M. A. (2011). Jacobian-free diagonal Newton’s method for solving nonlinear systems with singular Jacobian. Malaysian Journal of Mathematical Sciences, 5(2), 241-255.