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Numerical Methods for Equations and its Applications

By Ioannis K. Argyros, Yeol J. Cho, Saïd Hilout

CRC Press – 2012 – 474 pages

Purchasing Options:

  • Add to CartHardback: $93.95
    978-1-57808-753-2
    June 5th 2012

Description

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.

Contents

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

Name: Numerical Methods for Equations and its Applications (Hardback)CRC Press 
Description: By Ioannis K. Argyros, Yeol J. Cho, Saïd Hilout. 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,...
Categories: Computational Numerical Analysis, Mathematics & Statistics for Engineers, Applied Mathematics