Effective Algorithm for Solving Symmetric Nonlinear Equations

Jamilu Sabi'u

Abstract


In this article, eective and ecient solver for symmetric nonlinear equations without com-
puting exact gradient and Jacobian with a very low memory requirement is proposed. The
global convergence of the proposed method was also established under some rigorous condi-
tions with nonmonotone line search. Numerical experiment shows the proposed method is
ecient.


Full Text:

PDF

References


Cheng, W., Chen, Z. Nonmonotone Spectral method for large-Scale symmetric nonlin-

ear equations. Numer. Algorithms. 62:62149-162, 2013

Gu, G., Z., Li, D,-H., Qi, L., Zhou, S.-Z.Descent direction of quasi-Newton methods

for symmetric nonlinear equations. SIAM J. Numer. Anal. 40:1763-1774, 2002.

Zhang, L.,Zhou, W., Li, D.-H. Global convergence of a modied Fletcher-Reeves conju-

gate gradient method with Armijo-type line search. Numer. Math. 104:561-572, 2006.

Li, D.H., Fukushima. A globally and superlinearly convergent Gauss-Newton-based

BFGS methods for symmetric nonlinear equations. SIAM J. Numer. Anal. 37:152-172,

Li, D.-H., Wang, X. A modied Fletcher-Reeves-type derivative-free method for sym-

metric nonlinear equations. Numer. Algebra Control Optim.1:71-82, 2011.

W. ZhouA globally and R-linearly hybrid HS and PRP method and its inexact version

with applications. Numer. Math. 104: 561-572,2006.

Sumit S. and Biprajit N. A modied form of conjugate direction for general nonlinear

function and its convergence, Int. J. of comp. sci. and mathematics. 7: 25-31, 2005.

Yunhai, X., Chunjie,W., Soon, Y.W. Norm descent conjugate gradient method for

solving symmetric nonlinear equations, J. Glo. Optim.(2014) DOI 10.1007/s10898-014-

-7.

Yuan, G., Lu, X., Wei, Z.BFGS trust-region method for symmetric nonlinear equations.

J. Comput. Appl. Math.230:44-58, 2009.

Sabi'u J. Enhanced derivative-free conjugate gradient method for solving symmetric

nonlinear equations. International Journal of Advances in Applied Sciences 5(1) 2016.

]J. sabi'u, U. Sanusi. An ecient new conjugate gradient approach for solving symmetric

nonlinear equations , Asian Journal of Mathematics and Computer Research 12: 34-

,2016.

M.Y. Waziri, J. Sabi'u. A derivative-free conjugate gradient method and its global

convergence for solving symmetric nonlinear equations. International J. of mathematics

and mathematical science vol.(2015), doi:10.1155/2015/961487.

Hager W.W. ,Zhang H. A New conjugate gradient Method with Guaranteed Descent

and an ecient line search. SIAM J. Optim. 16:170-192, 2005.

M. Raydan. The Barzilai and Borwein gradient method for the large uncostrained

minimization problem. SIAM Journal on Optimization. 7: 26-33, 1997.

M.Y. Waziri, J. Sabiu. An alternative conjugate gradient approach for large-scale sym-

metric nonlinear equations. 6(5): 855, 2016.


Refbacks

  • There are currently no refbacks.