Sequence Transformations and Their Applications

Name: Sequence Transformations and Their Applications
Brand: Academic Press
Price: 80.95 EUR
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WIMP(Autor*in)

WIMP(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

279 Seiten

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Front Cover
Sequence Transformations and Their Applications
Copyright Page
Contents
Preface
Acknowledgments
Notation
Chapter 1. Sequences and Series
1.1 Order Symbols and Asymptotic Scales, Continuous Variables
1.2 Integer Variables
1.3 Sequences and Transformations in Abstract Spaces
1.4 Properties of Complex Sequences
1.5 Further Properties of Complex Sequences
1.6 Totally Monotone and Totally Oscillatory Sequences
1.7 Birkhoff-Poincaré Logarithmic Scales
Chapter 2. Linear Transformations
2.1 Toeplitz's Theorem in a Banach Space
2.2 Complex Toeplitz Methods
2.3 Important Triangles
2.4 Toeplitz Methods Applied to Series of Variable Terms
Fourier Series and Lebesgue Constants
2.5 Toeplitz Methods and Rational Approximations
The Padé Table
2.6 Other Orthogonal Methods
Pollaczek Polynomials and Padé Approximants
2.7 Other Methods for Generating Toeplitz Transformations
Chapter 3. Linear Lozenge Methods
3.1 Background: Richardson Extrapolation and Romberg Integration
3.2 General Deltoids
3.3 Deltoids Obtained by Extrapolation
3.4 Example: Quadrature Based on Cardinal Interpolation
3.5 General Rhombus Lozenges
Chapter 4. Optimal Methods and Methods Based on Power Series
4.1 Best Methods for Laplace Moment Sequences
4.2 Optimal Approximations in l1 and Rc
4.3 Methods Based on Power Series
Chapter 5. Nonlinear Lozenges
Iteration Sequences
5.1 General Theory of Nonlinear Lozenge Algorithms
5.2 Path Regularity for Certain Lozenges
5.3 Iteration Sequences
Chapter 6. The Schmidt Transformation
The e-Algorithm
6.1 Background
6.2 Derivation
6.3 Exactness Results
6.4 The Effect of ek on Certain Series
6.5 Power Series and ek
The Padé Table
6.6 Geometrical Significance of the Schmidt Transformation
6.7 The e-Algorithm
6.8 The Stability of the e-Algorithm
6.9 Rational Analogs of the Formulas of Numerical Analysis
6.10 Generalizations of the e-Algorithm
6.11 Fixed Points of Differentiable Functions
Chapter 7. Aitken's d2-Process and Related Methods
7.1 Aitken's d2-Process
7.2 The Lubkin W-Transform
7.3 Related Algorithms
Chapter 8. Lozenge Algorithms and the Theory of Continued Fractions
8.1 Background
8.2 The Quotient Difference Algorithm
The ?-Algorithm
Chapter 9. Other Lozenge Algorithms and Nonlinear Methods
9.1 A Multiparameter e-Algorithm
9.2 The p-Algorithm
9.3 The ?-Algorithm
9.4 Implicit Summation: Logarithmically Convergent Sequences
Chapter 10. The Brezinski-Håvie Protocol
10.1 Introduction and Derivation
Sequences in a Banach Space
10.2 The Case f Constant
10.3 The Topological Schmidt Transformation
10.4 The Scalar Case
10.5 The Levin Transformations
10.6 Special Computational Procedures: The Trench Algorithm
Chapter 11. The Brezinski-Håvie Protocol and Numerical Quadrature
11.1 Introduction
The G-Transform
11.2 The Computation of Fourier Coefficients
11.3 The tanh Rule
Chapter 12. Probabilistic Methods
12.1 Introduction
12.2 Derivation of the Methods
12.3 Properties of the Methods
12.4 Numerics
Chapter 13. Multiple Sequences
13.1 Rectangular Transformations
13.2 Crystal Lattice Sums
Appendix
A.1 Lagrangian Interpolation
A.2 The Formula for the e-Algorithm
A.3 Sylvester's Expansion Theorem
Bibliography
Index

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