[PDF] Top 20 A trust region spectral method for large scale systems of nonlinear equations

... the large-scale problem ...the spectral method for (). The method uses the residual ± F(x k ) as a search direction and the trial point at each iteration ... See full document

... new method has better results compared to Classical Broyden (CB) and the Trapezoidal Broyden method (TB) in terms of number of iterations and with regards to the CPU time, the method is competitive ... See full document

... integration method was successfully applied to solving nonlinear equa- ...The method is of same simplicity as fixed point iteration, but the efficiency has been significantly im- proved, so it is ... See full document

... In this section, numerical results are provided to substantiate the efficacy of the proposed method. The codes are written in Mablab Ra and run on a personal computer with . GHz CPU processor. For comparison, ... See full document

... For large-scale unconstrained optimization problems and nonlinear equations, we propose a new three-term conjugate gradient algorithm under the Yuan–Wei–Lu line search ...descent method ... See full document

... The first projection approach was suggested by Solodov and Svaiter (1998) and it showed the totally convergent of solving nonlinear problems. In this study, the new algorithm is used to solve the nonlinear ... See full document

... handling large-scale problems for which the Jacobian is either not available or requires a low amount storage, the best method is CG ...handling large- scale problems due to their ... See full document

... Gauss–Newton method, Levenberg– Marquardt method [20], trust-region methods, spectral gradient, and residual methods [10, 24] and conjugate gradient methods ...with ... See full document

... non-monotone spectral gradient method is given in reference [3], an active set projected trust region algorithm in ...gradient method, sub-gradient method, conjugate gra- dient ... See full document

... solve nonlinear system of equations is the line search strategy, the other method is trust ...search method and its framework. This method is fairly simple, so, its understanding ... See full document

... 38. Yuan, G., Wei, Z., Yang, Y.: The global convergence of the Polak–Ribiere–Polyak conjugate gradient algorithm under inexact line search for nonconvex functions. J. Comput. Appl. Math. (2018). ... See full document

... new method is de- creasing computational cost by combining two nonmonotone techniques and adaptive radius trust ...proposed method for solving systems of nonlinear ... See full document

... a trust-region algorithm combining with the limited memory BFGS (L-BFGS) update is proposed for solving nonlinear equations, where the super relaxation technique(SRT) is ...this method ... See full document

... with/without nonlinear mapping gives similar ...no nonlinear mapping, we have the possibility of directly solving bigger optimization ...our method cannot be ...our trust region ... See full document

... of trust region methods for solving systems of nonlinear equations has been popular during the past ...with trust region idea to solve nonlinear ...norm ... See full document

... solved equations (1-2) using regular perturbation method, asymptotic method so- lution, implicit finite difference method together with Keller-box scheme and local nonsimilarity ...difference ... See full document

... [3] Simon, B. (1999) A New Approach to Inverse Spectral Theory. I. F undamental Formalism. Annals of Mathematics , 150, 1029-1057. https://doi.org/10.2307/121061 [4] Gesztesy, F. (2007) Inverse Spectral ... See full document

... discrete-time large-scale nonlinear systems. The considered large-scale system is composed of a number of nonlinear subsystems and exchanges its information through ... See full document

... Nonlinear systems of equations appear in numerical applications ...The nonlinear systems of equations are usually difficult to solve, either exactly or numerically (Scheffel and ... See full document

... This paper contains an informal discussion of recent results concerning the well posedness of the Cauchy problem for a nonlinear system of conservation laws in one space dimension. The system is assumed to be ... See full document