Descent Derivative-Free Method Involving Symmetric Rank-One Update for Solving Convex Constrained Nonlinear Monotone Equations and Application to Image Recovery

A Rank-One Fitting Method with Descent Direction for Solving Symmetric Nonlinear Equations

In this paper, a rank-one updated method for solving symmetric nonlinear equations is proposed. This method possesses some features: 1) The updated matrix is positive definite whatever line search technique is used; 2) The search direction is descent for the norm function; 3) The global convergence of the given method is established under reasonable conditions. Numerical results show that the p...

New Efficient Optimal Derivative-Free Method for Solving Nonlinear Equations

In this paper, we suggest a new technique which uses Lagrange polynomials to get derivative-free iterative methods for solving nonlinear equations. With the use of the proposed technique and Steffens on-like methods, a new optimal fourth-order method is derived. By using three-degree Lagrange polynomials with other two-step methods which are efficient optimal methods, eighth-order methods can b...

Norm descent conjugate gradient methods for solving symmetric nonlinear equations

Nonlinear conjugate gradient method is very popular in solving large-scale unconstrained minimization problems due to its simple iterative form and lower storage requirement. In the recent years, it was successfully extended to solve higher-dimension monotone nonlinear equations. Nevertheless, the research activities on conjugate gradient method in symmetric equations are just beginning. This s...

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations

Dynamical systems method for solving nonlinear equations with monotone operators

A version of the Dynamical Systems Method (DSM) for solving ill-posed nonlinear equations with monotone operators in a Hilbert space is studied in this paper. An a posteriori stopping rule, based on a discrepancytype principle is proposed and justified mathematically. The results of two numerical experiments are presented. They show that the proposed version of DSM is numerically efficient. The...