1st Edition
Numerical Methods for Equations and its Applications
INTRODUCTION
NEWTON’S METHOD
Convergence under Fréchet differentiability. Convergence under twice Fréchet differentiability. Newton’s method on unbounded domains. Continuous analog of Newton’s method. Interior point techniques. Regular smoothness. ω-convergence. Semilocal convergence and convex majorants. Local convergence and convex majorants. Majorizing sequences.
SECANT METHOD
Convergence. Least squares problems. Nondiscrete induction and Secant method. Nondiscrete induction and a double step Secant method. Directional Secant Methods. Efficient three step Secant methods.
STEFFENSEN’S METHOD
Convergence
GAUSS-NEWTON METHOD
Convergence. Average-Lipschitz conditions.
NEWTON-TYPE METHODS
Convergence with outer inverses. Convergence of a Moser-type Method. Convergence with slantly differentiable operator. A intermediate Newton method.
INEXACT METHODS
Residual control conditions. Average Lipschitz conditions. Two-step methods. Zabrejko-Zincenko-type conditions.
WERNER’S METHOD
Convergence analysis
HALLEY’S METHOD
Local convergence
METHODS FOR VARIATIONAL INEQUALITIES
Subquadratic convergent method. Convergence under slant condition. Newton-Josephy method.
FAST TWO-STEP METHODS
Semilocal convergence
FIXED POINT METHODS
Successive substitutions methods
Biography
Argyros, Ioannis K.; Cho, Yeol J.; Hilout, Saïd
