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Sequence transformations and their applications /
Sequence transformations and their applications.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1981.
|
| Colección: | Mathematics in science and engineering ;
v. 154. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
Tabla de Contenidos:
- 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-Poincar�e Logarithmic Scales; Chapter 2. Linear Transformations; 2.1 Toeplitz's Theorem in a Banach Space; 2.2 Complex Toeplitz Methods
- 2.3 Important Triangles2.4 Toeplitz Methods Applied to Series of Variable Terms; Fourier Series and Lebesgue Constants; 2.5 Toeplitz Methods and Rational Approximations; The Pad�e Table; 2.6 Other Orthogonal Methods; Pollaczek Polynomials and Pad�e 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 Series4.1 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 Pad�e Table
- 6.6 Geometrical Significance of the Schmidt Transformation6.7 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-Algorithm9.2 The p-Algorithm; 9.3 The ?-Algorithm; 9.4 Implicit Summation: Logarithmically Convergent Sequences; Chapter 10. The Brezinski-H�avie 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-H�avie Protocol and Numerical Quadrature; 11.1 Introduction; The G-Transform; 11.2 The Computation of Fourier Coefficients; 11.3 The tanh Rule