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Laurent Series and their Padé Approximations

The Pade approximation problem is, roughly speaking, the local approximation of analytic or meromorphic functions by rational ones. It is known to be important to solve a large scale of problems in numerical analysis, linear system theory, stochastics and other fields. There exists a vast literature...

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Bibliographic Details
Main Author: Bultheel, A.
Format: eBook
Language:English
Published: Basel Birkhäuser 1987, 1987
Edition:1st ed. 1987
Series:Operator Theory: Advances and Applications
Subjects:
Humanities And Social Sciences
Humanities
Social Sciences
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 8.4 ?? paramaters (diagonal path)
  • 8.5 Some dual results
  • 8.6 Relation with classical algorithms
  • 9. Biorthogonal polynomials, quadrature and reproducing kernels
  • 9.1 Biorthogonal polynomials
  • 9.2 Interpolatory quadrature methods
  • 9.3 Reproducing kernels
  • 9.4 Other orthogonality relations
  • 10. Determinant expressions and matrix interpretations
  • 10.1 Determinant expressions
  • 10.2 Matrix interpretations
  • 11. Symmetry Properties
  • 11.1 Symmetry for F(z) and
  • 2. Introduction
  • 2.1 Classical Padé approximation
  • 2.2 Toeplitz and Hankel systems
  • 2.3 Continued fractions
  • 2.4 Orthogonal polynomials
  • 2.5 Rhombus algorithms and convergence
  • 2.6 Block structure
  • 2.7 Laurent-Padé approximants
  • 2.8 The projection method
  • 2.9 Applications
  • 2.10 Outline
  • 3. Moebius transforms, continued fractions and Padé approximants
  • 3.1 Moebius transforms
  • 3.2 Flow graphs
  • 3.3 Continued fractions (CF)
  • 3.4 Formal series
  • 3.5 Padé approximants
  • 4. Two algorithms
  • 4.1 Algorithm 1
  • 4.2 Algorithm 2
  • 5. All kinds of Padé Approximants
  • 5.1 Padé approximants
  • 5.2 Laurent-Padé approximants
  • 5.3 Two-point Padé approximants
  • 6. Continued fractions
  • 6.1 General observations
  • 6.2 Some special cases
  • 7. Moebius transforms
  • 7.1 General observations
  • 7.2 Some special cases
  • 8. Rhombus algorithms
  • 8.1 The ab parameters (sawtooth path)
  • 8.2. The FG parameters (row path)
  • 8.3. A staircase path

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