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E-book: Numerical Methods for Equations and its Applications

(Cameron University, Lawton, Oklahoma, USA), (Poitiers University, Futuroscope Chasseneuil Cedex, France), (Gyeongsang National University, Chinju, Korea)
  • Format: 474 pages
  • Pub. Date: 05-Jun-2012
  • Publisher: Science Publishers,U.S.
  • Language: eng
  • ISBN-13: 9781466517110
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Numerical Methods for Equations and its ApplicationsLarger Image
  • Format: 474 pages
  • Pub. Date: 05-Jun-2012
  • Publisher: Science Publishers,U.S.
  • Language: eng
  • ISBN-13: 9781466517110
Other books in subject:

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"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"--

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 v
1 Introduction 1(9)
2 Newton's Method 10(125)
2.1 Convergence Under Fr'echet Differentiability
10(28)
2.2 Convergence Under Twice Fr'echet Differentiability
38(13)
2.3 Newton's method on unbounded domains
51(8)
2.4 Continuous Analog of Newton's method
59(4)
2.5 Interior Point Techniques
63(7)
2.6 Regular smoothness
70(11)
2.7 ω-convergence
81(9)
2.8 Semilocal Convergence and Convex Majorants
90(12)
2.9 Local Convergence and Convex Majorants
102(8)
2.10 Majorizing Sequences
110(15)
2.11 Upper Bounds for Newton's Method
125(10)
3 Secant method 135(73)
3.1 Convergence
135(11)
3.2 Least Squares Problems
146(8)
3.3 Nondiscrete Induction and Secant Method
154(9)
3.4 Nondiscrete Induction and a Double Step Secant Method
163(12)
3.5 Directional Secant Methods
175(20)
3.6 Efficient Three Step Secant Methods
195(13)
4 Steffensen's Method 208(10)
4.1 Convergence
208(10)
5 Gauss-Newton method 218(32)
5.1 Convergence
218(10)
5.2 Average-Lipschitz Conditions
228(22)
6 Newton-type methods 250(43)
6.1 Convergence with Outer Inverses
250(14)
6.2 Convergence of a Moser-type Method
264(7)
6.3 Convergence with Slantly Differentiable Operator
271(8)
6.4 A intermediate Newton Method
279(14)
7 Inexact Methods 293(42)
7.1 Residual control Conditions
293(13)
7.2 Average Lipschitz Conditions
306(6)
7.3 Two-step Methods
312(14)
7.4 Zabrejko-Zincenko-type Conditions
326(9)
8 Werner's Method 335(9)
8.1 Convergence Analysis
335(9)
9 Halley's Method 344(9)
9.1 Local Convergence
344(9)
10 Methods for variational inequalities 353(32)
10.1 Subquadratic Convergent Method
353(7)
10.2 Convergence Under Slant Condition
360(9)
10.3 Newton-Josephy Method
369(16)
11 Fast two-step methods 385(14)
11.1 Semilocal Convergence
385(14)
12 Fixed Point Methods 399(16)
12.1 Successive Substitutions Methods
399(16)
Bibliography 415(48)
Index 463
Argyros, Ioannis K.; Cho, Yeol J.; Hilout, Saïd
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