[PDF] Top 20 A quasi Newton algorithm for large scale nonlinear equations

... inexact quasi-Newton methods with a new nonmonotone technique for solving smooth nonlinear ...our algorithm, the following new nonmonotone technique is used to obtain α k ... See full document

... However, it is a complex mathematic model since it needs to meet various conditions in the field [30–33]. Experts and scholars have conducted numerous in-depth studies and have made some significant achievements (see [14, ... See full document

... solving large-scale nonlinear equations (see ...BFGS quasi- Newton, and conjugate gradient methods can solve large-scale optimization problems and systems of ... See full document

... of equations, introduced new methods which although iterative in nature, were quite unlike any others in use at the ...a large amount of research in the late sixties and early ... See full document

... Further more, in table 2 we also report the behavior of the DDLS algorithm for problems 1, 2 and 5 with some different initial points, to illustrate the global convergence. For these problems, the solution vector ... See full document

... further improved by Gu et al. [3], where a norm descent BFGS methods are designed. Since then, norm descent type BFGS methods especially coorporating with trust regions strategy are presented in the literature and showed ... See full document

... Generally, there are two categories of solution methods for solving the problem. The first one is first-order methods including the trust region method, the Levenberg-Marquardt method and the projection method. The second ... See full document

... ∇ . Many researchers have studied constrained optimization problems such as (2) and given many effective algorithms. For example, a new class of adaptive non-monotone spectral gradient method is given in reference [3], ... See full document

... solving nonlinear equations, such as high sensitivity to the initial guess of the solution, poor convergence reliability and can’t get all solutions, ...new Quasi-Newton Population Migration ... See full document

... 197, 237, 259 respectively. As compared with Newton method the corresponding figures are 34, 45, 100 [7]. Our goal is not to compare those two sets of figure, as we said before, the main work for Newton ... See full document

... For nonlinear equations, Griewank [25] first estab- lished a global convergence theorem for quasi-Newton method with a suitable line ...inexact quasi-Newton algorithm [26] ... See full document

... solving nonlinear problems. In this study, the new algorithm is used to solve the nonlinear systems, we proved its global ...new algorithm will be more ... See full document

... the nonlinear equations by using a classical method and a powerful ...use Newton-HCM to solve the divergence problem that the classical Newton’s method always ...of Newton-HCM to solve this ... See full document

... In this section, we develop some preconditioned iterative methods for solving systems of nonlinear equations. We generalize the idea of preconditioning in such a way that the quadratic convergence will be ... See full document

... Truncated Newton methods have been an effective approach for large-scale unconstrained op- timization, but their use for logistic regression has not been fully ...truncated Newton method for ... See full document

... memoryless quasi- Newton method where at each iteration the inverse Hessian approximation is restarted as a multiple of the identity matrix with a positive scaling parameter ... See full document

... very large data set and it is useful to discover the correlation among attributes both of spherical and non spherical shape which is also robust to ...very large data sets which help to find the ... See full document

... training algorithm in which second order derivative information is ...The algorithm involves matrix ...training algorithm proves more useful for small and medium scale neural ...The ... See full document

... The organization of the paper is as follows. In Section 2 a concise descrip- tion of the Newton Method, the Homotopy Method are presented. In Section 3 the fundamental of HAM and proposed approach is discussed. In ... See full document

... of nonlinear equations will be solved using the combinations of Newton, conjugate gradient and quadrature ...of Newton and conjugate gradient where it is called preconditioned conjugate ... See full document