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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:
Acceso en línea:Texto completo
Texto completo
Texto completo

MARC

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100 1 |a Bultheel, Adhemar. 
245 1 0 |a Linear algebra, rational approximation, and orthogonal polynomials /  |c Adhemar Bultheel, Marc van Barel. 
260 |a Amsterdam ;  |a New York :  |b Elsevier,  |c 1997. 
300 |a 1 online resource (xvii, 446 pages) :  |b illustrations 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a Studies in computational mathematics ;  |v 6 
520 |a 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 fast algorithms for structured problems and shows how they deal with singular situations. Links are made with more applied subjects such as linear system theory and signal processing, and with more advanced topics and recent results such as general bi-orthogonal polynomials, minimal Pa�d approximation, polynomial root location problems in the complex plane, very general rational interpolation problems, and the lifting scheme for wavelet transform computation. The text serves as a supplement to existing books on structured linear algebra problems, rational approximation and orthogonal polynomials. Features of this book: & bull; provides a unifying approach to linear algebra, rational approximation and orthogonal polynomials & bull; requires an elementary knowledge of calculus and linear algebra yet introduces advanced topics. The book will be of interest to applied mathematicians and engineers and to students and researchers. 
504 |a Includes bibliographical references (pages 413-433) and index. 
588 0 |a Print version record. 
505 0 |a 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. 
650 0 |a Euclidean algorithm. 
650 0 |a Algebras, Linear. 
650 0 |a Pad�e approximant. 
650 0 |a Orthogonal polynomials. 
650 6 |a Algorithme d'Euclide.  |0 (CaQQLa)201-0270600 
650 6 |a Alg�ebre lin�eaire.  |0 (CaQQLa)201-0001189 
650 6 |a Approximants de Pad�e.  |0 (CaQQLa)201-0021341 
650 6 |a Polyn�omes orthogonaux.  |0 (CaQQLa)201-0011281 
650 7 |a MATHEMATICS  |x Number Theory.  |2 bisacsh 
650 7 |a Algebras, Linear  |2 fast  |0 (OCoLC)fst00804946 
650 7 |a Euclidean algorithm  |2 fast  |0 (OCoLC)fst00916406 
650 7 |a Orthogonal polynomials  |2 fast  |0 (OCoLC)fst01048521 
650 7 |a Pad�e approximant  |2 fast  |0 (OCoLC)fst01050307 
700 1 |a Barel, Marc van,  |d 1960- 
776 0 8 |i Print version:  |a Bultheel, Adhemar.  |t Linear algebra, rational approximation, and orthogonal polynomials.  |d Amsterdam ; New York : Elsevier, 1997  |z 0444828729  |z 9780444828729  |w (DLC) 97040610  |w (OCoLC)37682686 
830 0 |a Studies in computational mathematics ;  |v 6. 
856 4 0 |u https://sciencedirect.uam.elogim.com/science/book/9780444828729  |z Texto completo 
856 4 0 |u https://sciencedirect.uam.elogim.com/science/publication?issn=1570579X&volume=6  |z Texto completo 
856 4 0 |u https://sciencedirect.uam.elogim.com/science/bookseries/1570579X/6  |z Texto completo