Advances In The Efficiency Of Computational Methods And Applications - Ioannis K. Argyros

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Advances In The Efficiency Of Computational Methods And Applications

By: Ioannis K. Argyros

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Hardcover | 26 July 2000

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560 Pages

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22.86 x 16.51 x 3.81

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This invaluable textbook creates a general framework for the study of optimal iterative procedures for problems that are solved approximately. Emphasis is given to the efficiency of numerical methods. For generality the setting is abstract, but the book presents many applications to practical problems, allowing the reader to take advantage of the most modern high speed calculating devices, and provides examples to illustrate concepts and major theorems. The examples are selected from astrophysics (radiative transfer and the kinetic theory of gases), mechanics (elasticity), economics (predator -- prey problems), the n-dimensional Euclidean space and other applied areas.The book will benefit not only senior undergraduates, graduates, graduate students and researchers in the field but also those who wish to obtain information about specific results or techniques that take into account the particular nature of the equation.

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Preface	p. vii
Divided Differences	p. 1
Partially Ordered Topological Spaces	p. 1
Divided Difference in a Linear Space	p. 4
Divided Differences in a Banach Space	p. 5
Divided Differences and Monotone Convergence	p. 11
Divided Differences and Frechet-derivatives	p. 16
Exercises	p. 21
Constants and Functions Appearing in Numerical Methods	p. 29
Preliminaries	p. 29
Lipschitz Conditions and Norm Estimate	p. 34
Lipschitz Conditions for Uryson Operators	p. 36
The Case X = C	p. 39
The Case X = L[infinity]	p. 41
The Case X = Lp, 1 [left than or equal] p [left than or equal] 2	p. 43
The Case X = Lp, 2 [ p [ [infinity]	p. 44
Exercises	p. 46
Convergence and Error Analysis for Iterative Methods	p. 57
Preliminaries	p. 59
A Unified Approach for Constructing Inexact Newton-Like Methods	p. 61
Semilocal Convergence Results for Newton-Like Methods	p. 80
A Fixed Point Proof for Extended Newton-Like Methods	p. 90
A Generalization of Edelstein's Theorem on Fixed Points	p. 97
Weak Conditions for the Convergence of Iterations	p. 102
Monotone Convergence of Implicit Newton-Like Methods	p. 108
General Ways of Constructing Accelerating Newton-Like Iterations	p. 113
A Generalization of Ostrowski's Theorem on Fixed Points	p. 117
Exercises	p. 120
Special Topics	p. 155
Convergence Rates for Inexact Newton-Like Methods at Singular Points	p. 155
Smoothness and Inexact Newton-Like Methods	p. 171
Convergence Domains Using Outer or Generalized Inverses	p. 185
Exercises	p. 203
Convergence in Generalized Banach Spaces	p. 207
Convergence of Inexact Newton-Like Methods with a Convergence Structure	p. 207
Improving the Rate of Convergence	p. 218
Controlling the Residuals of Inexact Newton-Like Methods	p. 222
Exercises	p. 231
Discretization of Newton-Like Methods	p. 247
The Mesh Independence Principle for Inexact Newton-Like Methods	p. 247
A New Newton--Mysovskii-Type Theorem	p. 275
Inexact Newton--Galerkin-Like Methods	p. 296
Exercises	p. 317
Convergence Analysis Based on the Second Frechet-Derivative	p. 323
A New Convergence Theorem Based on the Second Frechet-Derivative	p. 323
Improved Error Bounds	p. 331
A New Kantorovich-Type Theorem Involving First and Second Derivatives	p. 340
Newton-Like Methods Using Twice Frechet Differentiable Operators	p. 347
The Convergence of Newton's Method for Polynomial Equations	p. 356
Uniform-Like Continuity Conditions	p. 368
A Global Convergence Theorem	p. 376
Semilocal Convergence Theorems	p. 381
Semilocal Convergence Theorems II	p. 390
Local Convergence Theorems	p. 397
Monotone Convergence and Divided Differences of Order Two	p. 406
Exercises	p. 412
Forcing Sequences and the Second Frechet-Derivative	p. 419
Relations Between Forcing Sequences and Inexact Newton Iterates	p. 419
Affine Invariant Local Convergence Theorems for Inexact Newton-Like Methods	p. 432
The Radius of Convergence of Newton's Method	p. 444
Local Convergence Involving the Second Frechet-Derivative	p. 455
Choosing Forcing Sequences	p. 463
Rounding Errors	p. 472
Convergence and Residuals	p. 478
Relations Between Forcing Sequences and Inexact Newton-Like Iterates	p. 487
Exercises	p. 495
Numerical Algorithms	p. 503
References	p. 527
Glossary of Symbols	p. 543
Index	p. 545
Table of Contents provided by Syndetics. All Rights Reserved.

Advances In The Efficiency Of Computational Methods And Applications

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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