1st Edition

Numerical Methods for Equations and its Applications

    This book introduces advanced numerical-functional analysis to beginning computer science researchers. The reader is assumed to have had basic courses in numerical analysis, computer programming, computational linear algebra, and an introduction to real, complex, and functional analysis. Although the book is of a theoretical nature, each chapter contains several new theoretical results and important applications in engineering, in dynamic economics systems, in input-output system, in the solution of nonlinear and linear differential equations, and optimization problem.

    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