Linear algebra, rational approximation, and orthogonal polynomials /

Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, non-normal Pa�d tables, look-ahead algorithms for Hankel and Toeplitz matrices, and for Krylov subspace methods. It introduces the basics of...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Bultheel, Adhemar
Otros Autores: Barel, Marc van, 1960-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Amsterdam ; New York : Elsevier, 1997.
Colección:Studies in computational mathematics ; 6.
Temas:
Euclidean algorithm.
Algebras, Linear.
Pad�e approximant.
Orthogonal polynomials.
Algorithme d'Euclide.
Alg�ebre lin�eaire.
Approximants de Pad�e.
Polyn�omes orthogonaux.
MATHEMATICS > Number Theory.
Algebras, Linear
Euclidean algorithm
Orthogonal polynomials
Pad�e approximant
Acceso en línea:Texto completo
Texto completo
Texto completo
Tabla de Contenidos:
  • Cover
  • Contents
  • Preface
  • List of symbols
  • Chapter 1. Euclidean fugues
  • 1.1 The algorithm of Euclid
  • 1.2 Euclidean ring and g.c.l.d
  • 1.3 Extended Euclidean algorithm
  • 1.4 Continued fraction expansions
  • 1.5 Approximating formal series
  • 1.6 Atomic Euclidean algorithm
  • 1.7 Viscovatoff algorithm
  • 1.8 Layer peeling vs. layer adjoining methods
  • 1.9 Left-Riight duality
  • Chapter 2. Linear algebra of Hankels
  • 2.1 Conventions and notations
  • 2.2 Hankel matrices
  • 2.3 Tridiagonal matrices
  • 2.4 Structured Hankel information
  • 2.5 Block Gram-Schmidt algorithm
  • 2.6 The Schur algorithm
  • 2.7 The Viscovatoff algorithm
  • Chapter 3. Lanczos algorithm
  • 3.1 Krylov spaces
  • 3.2 Biorthogonality
  • 3.3 The generic algorithm
  • 3.4 The Euclidean Lanczos algorithm
  • 3.5 Breakdown
  • 3.6 Note of warning
  • Chapter 4. Orthogonal polynomials
  • 4.1 Generalities
  • 4.2 Orthogonal polynomials
  • 4.3 Properties
  • 4.4 Hessenberg matrices
  • 4.5 Schur algorithm
  • 4.6 Rational approximation
  • 4.7 Generalization of Lanczos algorithm
  • 4.8 The Hankel case
  • 4.9 Toeplitz case
  • 4.10 Formal orthogonality on an algebraic curve
  • Chapter 5. Pade approximation
  • 5.1 Definitions and terminology
  • 5.2 Computation of diagonal PAs
  • 5.3 Computation of antidiagonal PAs
  • 5.4 Computation of staircase PAs
  • 5.5 Minimal indices
  • 5.6 Minimal Pad�e approximation
  • 5.7 The Massey algorithm
  • Chapter 6. Linear systems
  • 6.1 Definitions
  • 6.2 More definitions and properties
  • 6.3 The minimal partial realization problem
  • 6.4 Interpretation of the Pad�e results
  • 6.5 The mixed problem
  • 6.6 Interpretation of the Toeplitz results
  • 6.7 Stability checks
  • Chapter 7. General rational interpolation
  • 7.1 General framework
  • 7.2 Elementary updating and downdating steps
  • 7.3 A general recurrence step
  • 7.4 Pad�e approximation
  • 7.5 Other applications
  • Chapter 8. Wavelets
  • 8.1 Interpolating subdivisions
  • 8.2 Multiresolution
  • 8.3 Wavelet transforms
  • 8.4 The lifting scheme
  • 8.5 Polynomial formulation
  • 8.6 Euclidean domain of Laurent polynomials
  • 8.7 Factorization algorithm
  • Bibliography
  • List of Algorithms
  • Index
  • Last Page.

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