iterative methods for linear & nonlinear equations kelley [pdf]
Iterative Methods for Linear and Nonlinear Equations by C. T. Kelley
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About this book :-
C. T. Kelley.
This book on unconstrained and bound constrained optimization can be used as a tutorial for self-study or a reference by those who solve such problems in their work. It can also serve as a textbook in an introductory optimization course.
This book covers some algorithms for noisy or global optimization or both. There are many interesting algorithms in this class, and this book is limited to those deterministic algorithms that can be implemented in a more-or-less straightforward way. We do not, for example, cover simulated annealing, genetic algorithms, response surface methods, or random search procedures.
Book Detail :-
Title: Numerical Analysis
Author(s): C. T. Kelley
Publisher: Society for Industrial and Applied Mathematics
Series: Frontiers in applied mathematics
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About Author :-
The author C. T. Kelley, is a Drexel Professor of Mathematics at Department of Mathematics, North Carolina State University, where he has been on the faculty since 1978. He is the author of four books and over 100 papers and has mentored 18 PhD students.
He has complete his B.S.Vanderbilt University, Mathematics in 1973 and Ph.D. Purdue University, Applied Mathematics in 1976.
Kelley's area of research are linear and nonlinear equations, multilevel methods, large-scale and multi-model optimization, flow in porous media, nano-scale electronics and sensing, radiative and neutron transfer, optimal control, integral equations, partial differential equations, and computational quantum chemistry and physics.
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Book Contents :-
C. T. Kelley
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
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
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
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
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
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