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Numerical methods for equations and its applications

Author: Ioannis K Argyros; Yeol Je Cho; Said Hilout
Publisher: Boca Raton : CRC Press, ©2012.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"This monograph is intended for researchers in computational sciences, and as a reference book for an advanced numerical-functional analysis or computer science course. The goal is to introduce these powerful concepts and techniques at the earliest possible stage. The reader is assumed to have had basic courses in numerical analysis, computer programming, computational linear algebra, and an introduction to real,  Read more...
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Document Type: Book
All Authors / Contributors: Ioannis K Argyros; Yeol Je Cho; Said Hilout
ISBN: 9781578087532 1578087538
OCLC Number: 773024884
Description: viii, 465 pages : illustrations ; 24 cm
Contents: 1. Introduction --
2. Newton's method --
Convergence under Fr'echet differentiability --
Convergence under twice Fr'echet differentiability --
Newton's method on unbounded domains --
Continuous analog of Newton's method --
Interior point techniques --
Regular smoothness --
[Omega]-convergence --
Semilocal convergence and convex majorants --
Local convergence and convex majorants --
Majorizing sequences --
Upper bounds for Newton's method --
3. 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 --
4. Steffensen's method --
Convergence --
5. Gauss-Newton method --
Convergence --
Average-Lipschitz conditions --
6. Newton-type methods --
Convergence with outer inverses --
Convergence of a Moser-type method --
Convergence with slantly differentiable operator --
A intermediate Newton method --
7. Inexact methods --
Residual control conditions --
Average Lipschitz conditions --
Two-step methods --
Zabrejko-Zincenko-type conditions --
8. Werner's method --
Convergence analysis --
9. Halley's method --
Local convergence --
10. Methods for variational inequalities --
Subquadratic convergent method --
Convergence under slant condition --
Newton-Josephy method --
11. Fast two-step methods --
Semilocal convergence --
12. Fixed point methods --
Successive substitutions methods.
Responsibility: Ioannis K. Argyros, Yeol Je Cho, Saïd Hilout.
More information:

Abstract:

"This monograph is intended for researchers in computational sciences, and as a reference book for an advanced numerical-functional analysis or computer science course. The goal is to introduce these powerful concepts and techniques at the earliest possible stage. 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, with optimization and weakening of existing hypotheses considerations 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"--

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