高效计算模式及应用前沿ADVANCES IN THE EFFICIENCY OF COMPUTATIONAL METHODS AND APPLICATIONS

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Preface
Chapter 1 Divided Differences
1.1 Partially Ordered Topological Spaces
1.2 Divided Difference in a Linear Space
1.3 Divided Differences in a Banach Space
1.4 Divided Differences and Monotone Convergence
1.5 Divided Differences and Fr@chet-derivatives
1.6 Exercises
Chapter 2 Constants and Functions Appearing in Numerica Methods
2.1 Preliminaries 2!
2.2 Lipschitz Conditions and Norm Estimate 3,
2.3 Lipschitz Conditions for Uryson Operators 3q
2.4 The Case X = C 3!
2.5 The Case X -- Lc~ 4:
2.6 The CaseX=Lp, l 2.7 The Case X = Lp, 2 < p <
2.8 Exercises
Chapter 3 Convergence and Error Analysis for odsIterative Meth-
3.1 Preliminaries
3.2 A Unified Approach for Constructing Inexact Newton-Like Meth- ods
3.3 Semilocal Convergence Results for Newton-Like Methods
3.4 A Fixed Point Proof for Extended Newton-Like Methods . . .
3.5 A Generalization of Edelstein's Theorem on Fixed Points . . .
3.6 Weak Conditions for the Convergence of Iterations
3.7 Monotone Convergence of Implicit Newton-Like Methods . . .
3.8 General Ways of Constructing Accelerating Newton-Like Itera- tions
3.9 A Generalization of Ostrowski's Theorem on Fixed Points . . .
3.10 Exercises
Chapter 4 Special Topics
4.1 Convergence Rates for Inexact Newton-Like Methods at Singu-
lar Points
4.2 Smoothness and Inexact Newton-Like Methods
4.3 Convergence Domains Using Outer or Generalized Inverses . .
4.4 Exercises
Chapter 5 Convergence in Generalized Banach Spaces
5.1 Convergence of Inexact Newton-Like Methods with a Conver gence Structure
5.2 Improving the Rate of Convergence
5.3 Controlling the Residuals of Inexact Newton-Like Methods
5.4 Exercises
Chapter 6 Discretization of Newton-Like Methods
6.1 The Mesh Independence Principle for Inexact Newton-Like Meth ods
6.2 A New Newton-Mysovskii-Type Theorem
6.3 Inexact Newton-Galerkin-Like Methods
6.4 Exercises
Chapter 7 Convergence Analysis Based on the Second Frchet-Derivative
7.1 A New Convergence Theorem Based on the Second Fr~ch Derivative
7.2 Improved Error Bounds
……
Chapter 8 Forcing Sequences and the Second Frechet-Deri-vative
Appendix A Numerical Algorithms
References
Glossary of Symbols
Index