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.
Preface
Chapter 1 : Introduction
Part I : Newton’s Method
Chapter 2 : Convergence Under Fréchet Differentiability
Chapter 3 : Convergence Under Twice Fréchet Differentiability
Chapter 4 : Newton’s Method on Unbounded Domains
Chapter 5 : Continuous Analog of Newton’s Method
Chapter 6 : Interior Point Techniques
Chapter 7 : Regular Smoothness
Chapter 8 : Ω-Convergence
Chapter 9 : Semilocal Convergence and Convex Majorants
Chapter 10 : Local Convergence and Convex Majorants
Chapter 11 : Majorizing Sequences
Part II : Secant Method
Chapter 12 : Convergence
Chapter 13 : Least Squares Problems
Chapter 14 : Nondiscrete Induction and Secant Method
Chapter 15 : Nondiscrete Induction and a Double Step Secant Method
Chapter 16 : Directional Secant Methods
Chapter 17 : Efficient Three Step Secant Methods
Part III : Steffensen’s Method
Chapter 18 : Convergence
Part IV : Gauss-Newton Method
Chapter 19 : Convergence
Chapter 20 : Average-Lipschitz Conditions
Part V : Newton-Type Methods
Chapter 21 : Convergence With Outer Inverses
Chapter 22 : Convergence of a Moser-Type Method
Chapter 23 : Convergence With Slantly Differentiable Operator
Chapter 24 : A Intermediate Newton Method
Part VI : Inexact Methods
Chapter 25 : Residual Control Conditions
Chapter 26 : Average Lipschitz Conditions
Chapter 27 : Two-Step Methods
Chapter 28 : Zabrejko-Zincenko-Type Conditions
Part VII : Werner’s Method
Chapter 29 : Convergence Analysis
Part VIII : Halley’s Method
Chapter 30 : Local Convergence
Part IX : Methods For Variational Inequalities
Chapter 31 : Subquadratic Convergent Method
Chapter 32 : Convergence Under Slant Condition
Chapter 33 : Newton-Josephy Method
Part X : Fast Two-Step Methods
Chapter 34 : Semilocal Convergence
Part XI : Fixed Point Methods
Chapter 35 : Successive Substitutions Methods
Index
