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Iterative Methods for Linear and Nonlinear Equations by C. T. Kelley

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Iterative Methods for Linear and Nonlinear Equations written by by C. T. Kelley North Carolina State University . This is an other book of mathematics cover the following topics.

  • Basic Concepts and Stationary Iterative Methods
    Review and notation, The Banach Lemma and approximate inverses, The spectral radius, Matrix splittings and classical stationaryiterative methods, Exercises on stationaryiterative methods
  • Conjugate Gradient Iteration
    Krylov methods and the minimization property, Consequences of the minimization property, Termination of the iteration, Implementation, Preconditioning, CGNR and CGNE, Examples for preconditioned conjugate iteration, Exercises on conjugate gradient
  • GMRES Iteration
    The minimization propertyand its consequences, Termination, Preconditioning, GMRES implementation: Basic ideas, Implementation: Givens rotations, Other methods for nonsymmetric systems (Bi-CG, CGS, Bi-CGSTAB, TFQMR), Examples for GMRES iteration, Examples for CGNR, Bi-CGSTAB, and TFQMR iteration, Exercises on GMRES
  • Basic Concepts and Fixed-Point Iteration
    Types of convergence, Fixed-point iteration, The standard assumptions
  • Newton’s Method
    Local convergence of Newton’s method, Termination of the iteration, Implementation of Newton’s method, Errors in the function and derivative (The chord method, Approximate inversion of F, The Shamanskii method, Difference approximation to F, The secant method), The Kantorovich Theorem, Examples for Newton’s method, Exercises on Newton’s method
  • Inexact Newton Methods
    The basic estimates (Direct analysis, Weighted norm analysis, Errors in the function), Newton-iterative methods (Newton GMRES, Other Newton-iterative methods), Newton-GMRES implementation, Examples for Newton-GMRES (Chandrasekhar H-equation, Convection-diffusion equation), Exercises on inexact Newton methods
  • Broyden’s method
    The Dennis–Mor´e condition, Convergence analysis (Linear problems, Nonlinear problems), Implementation of Broyden’s method, Examples for Broyden’s method (Linear problems, Nonlinear problems), Exercises on Broyden’s method
  • Global Convergence
    Single equations, Analysis of the Armijo rule, Implementation of the Armijo rule (Polynomial line searches, Broyden’s method), Examples for Newton–Armijo (Inverse tangent function, Convection-diffusion equation, Broyden–Armijo), Exercises on global convergence
  • Bibliography
  • Index
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