HIGH ORDER ITERATIVE METHODS FOR DECOMPOSITION‐COORDINATION PROBLEMS

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Iterative methods for Robbins problems

Preconditioned iterative methods are described for the solution of an elliptic partial differential equation over an unit square region with Robbins boundary conditions. Transform based preconditioners are constructed and analyzed. The motivation is to exploit the fast inversion of transform based systems via the fast transform. We prove that transform based preconditioners can be chosen so tha...

iterative methods for equilibrium problems, variational inequalities and fixed points

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

Root finding by high order iterative methods based on quadratures

We discuss a recursive family of iterative methods for the numerical approximation of roots of nonlinear functions in one variable. These methods are based on Newton-Cotes closed quadrature rules. We prove that when a quadrature rule with n+ 1 nodes is used the resulting iterative method has convergence order at least n+ 2, starting with the case n = 0 (which corresponds to the Newton’s method).