MODIFICATION OF PSB QUASI-NEWTON UPDATE AND ITS GLOBAL CONVERGENCE FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS (FUDMA JOURNAL OF SCIENCES, 2021)
Nonlinear problems mostly emanate from the work of engineers, physicists, mathematicians and many other scientists. A variety of iterative methods have been developed for solving large scale nonlinear systems of equations. A prominent method for solving such equations is the classical Newton’s method, but it has many shortcomings that include computing Jacobian inverse that sometimes fails. To overcome such drawbacks, an approximation with derivative free line is used on an existing method. The method uses PSB (Powell-Symmetric Broyden) update. The efficiency of the proposed method has been improved in terms of number of iteration and CPU time, hence the aim of this research. The preliminary numerical results show that the proposed method is practically efficient when applied on some benchmark problems.
Keywords: Conjugate Gradient, Quasi-Newton, PSB, Nonlinear Equations