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Padé approximants:

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Bibliographic Details
Main Authors:	Baker, George A. 1932- (Author), Graves-Morris, Peter R. (Author)
Format:	Book
Language:	English
Published:	Cambridge [u.a.] Cambridge Univ. Press 1996
Edition:	2. ed.
Series:	Encyclopedia of mathematics and its applications 59
Subjects:	Padé-Näherung
Online Access:	Inhaltsverzeichnis
Physical Description:	XIV, 746 S. graph. Darst.
ISBN:	0521450071

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MARC


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adam_text	ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS PADE APPROXIMANTS SECOND EDITION GEORGE A. BAKER, JR. THEORETICAL DIVISION LOS ALAMOS NATIONAL LABORATORY PETER GRAVES-MORRIS DEPARTMENT OF MATHEMATICS UNIVERSITY OF BRADFORD CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE PAGE XI PREFACE TO THE FIRST EDITION XIII 1 INTRODUCTION AND DEFINITIONS 1 1.1 INTRODUCTION AND NOTATIONAL CONVENTIONS 1 1.2 PADE APPROXIMANTS TO THE EXPONENTIAL FUNCTION 8 1.3 SEQUENCES AND SERIES; OBSTACLES 15 1.4 THE BAKER DEFINITION, THE C-TABLE, AND BLOCK STRUCTURE 20 1.5 DUALITY AND INVARIANCE 32 2 ELEMENTARY DEVELOPMENTS 38 2.1 NUMERICAL CALCULATION OF PAD6 APPROXIMANTS 38 2.2 DECIPHERMENT OF SINGULARITIES FROM PADE APPROXIMANTS AND APPARENT ERRORS 44 2.3 SOME EXPLICIT FORMS FOR PADE DENOMINATORS 56 2.4 BIGRADIENTS AND HADAMARD S FORMULA 62 3 PADE APPROXIMANTS AND NUMERICAL METHODS 67 3.1 AITKEN S A 2 METHOD AS [L/L] PADE APPROXIMANTS 67 3.2 ACCELERATION AND OVERACCELERATION OF CONVERGENCE 71 3.3 THE E-ALGORITHM AND THE RJ- ALGORITHM 73 3.4 WYNN S IDENTITY AND THE E-ALGORITHM 81 3.5 COMMON IDENTITIES AND RECURSION FORMULAS 85 3.6 RECURSIVE CALCULATION OF THE COEFFICIENTS OF PAD6 APPROXIMANTS 92 3.7 KRONECKER S ALGORITHM AND CORDELLIER S IDENTITY 106 3.8 THE Q.D. ALGORITHM AND THE ROOT PROBLEM / 115 4 CONNECTION WITH CONTINUED FRACTIONS / 122 4.1 DEFINITIONS, RECURSION RELATIONS, AND COMPUTATION 122 4.2 CONTINUED FRACTIONS DERIVED FROM MACLAURIN SERIES 129 4.3 VARIOUS REPRESENTATIONS OF CONTINUED FRACTIONS 141 4.4 THE BERLEKAMP-MASSEY ALGORITHM AND AN APPLICATION OF IT 153 4.5 DIFFERENT TYPES OF CONTINUED FRACTIONS 165 4.6 EXAMPLES OF CONTINUED FRACTIONS WHICH ARE PADE APPROXIMANTS 173 4.7 CONVERGENCE OF CONTINUED FRACTIONS 182 VIII CONTENTS 5 STIELTJES SERIES AND POLYA SERIES 193 5.1 INTRODUCTION TO STIELTJES SERIES 193 5.2 CONVERGENCE OF STIELTJES SERIES 201 5.3 MOMENT PROBLEMS AND ORTHOGONAL POLYNOMIALS 213 5.4 STIELTJES SERIES CONVERGENT IN Z \| R 220 5.4.1 HAUSDORFF MOMENT PROBLEM 233 5.4.2 INTEGER MOMENT PROBLEM 234 5.5 STIELTJES SERIES WITH ZERO RADIUS OF CONVERGENCE 236 5.6 HAMBURGER SERIES AND THE HAMBURGER MOMENT PROBLEM 245 5.7 POLYA FREQUENCY SERIES 264 6 CONVERGENCE THEORY 276 6.1 INTRODUCTION TO CONVERGENCE THEORY. ROWS 276 6.2 DE MONTESSUS S THEOREM 280 6.3 HERMITE S FORMULA AND DE MONTESSUS S THEOREM 290 6.4 UNIQUENESS OF CONVERGENCE 297 6.5 CONVERGENCE IN MEASURE 305 6.6 LEMNISCATES, CAPACITY, AND MEASURE 316 6.7 THE PADE CONJECTURE 330 7 EXTENSIONS OF PADE APPROXIMANTS 335 7.1 MULTIPOINT PADE APPROXIMANTS 335 7.2 BAKER-GAMMEL APPROXIMANTS 362 7.3 SERIES ANALYSIS 372 7.4 PAD6-LAURENT, PADE-FOURIER, AND PADE-TCHEBYCHEFF APPROXIMANTS 378 7.5 LAURENT-PAD6 APPROXIMATION AND TOEPLITZ SYSTEMS 389 7.6 MULTIVARIABLE APPROXIMANTS 402 8 MULTISERIES APPROXIMANTS 415 8.1 SIMULTANEOUS PADE APPROXIMANTS 415 8.2 OPERATOR PADE APPROXIMANTS 429 8.3 RECTANGULAR MATRIX PADE APPROXIMANTS FOR MINIMAL PARTIAL- REALIZATION PROBLEMS 442 8.4 VECTOR PADE APPROXIMANTS 466 8.4.1 FUNCTIONAL PADE APPROXIMANTS 492 8.5 HERMITE-PADE POLYNOMIALS 494 8.5.1 MINIMALITY DEFINITIONS AND UNIQUENESS 497 8.5.2 TABLE STRUCTURE RESULTS 501 8.5.3 RECURSION RELATIONS 515 8.5.4 EXISTENCE OF SEQUENCES AND THE MODIFIED MINIMALITY DEFINITION 521 8.6 INTEGRAL AND ALGEBRAIC APPROXIMANTS 524 8.6.1 MONODROMY THEORY 525 8.6.2 DEFINITIONS AND THE ACCURACY-THROUGH-ORDER PRINCIPLE 531 8.6.3 EQUIVALENCE PROPERTIES 538 8.6.4 INVARIANCE PROPERTIES 539 8.6.5 SEPARATION PROPERTIES 543 8.6.6 CONVERGENCE THEORY 544 8.6.7 SINGULAR INDEX AND AMPLITUDE COMPUTATIONS 564 9 CONNECTION WITH INTEGRAL EQUATIONS AND QUANTUM MECHANICS 570 9.1 THE GENERAL METHOD AND FINITE-RANK KERNELS 570 CONTENTS IX 9.2 PADE APPROXIMANTS AND INTEGRAL EQUATIONS WITH COMPACT KERNELS 573 9.3 PROJECTION TECHNIQUES 578 9.4 POTENTIAL SCATTERING 584 9.5 DERIVATION OF PADE APPROXIMANTS FROM VARIATIONAL PRINCIPLES 596 9.6 AN ERROR BOUND ON PADE APPROXIMANTS FROM VARIATIONAL PRINCIPLES 606 9.7 SINGLE-SIGN POTENTIALS IN SCATTERING THEORY ETC. 608 9.8 VARIATIONAL PADE APPROXIMANTS 616 9.9 SINGULAR POTENTIALS 622 10 CONNECTION WITH NUMERICAL ANALYSIS 628 10.1 ACCELERATION OF CONVERGENCE 628 10.2 TCHEBYCHEFFS INEQUALITIES FOR THE DENSITY FUNCTION 633 10.3 COLLOCATION AND THE R-METHOD 639 10.4 CRANK-NICHOLSON AND RELATED METHODS FOR THE DIFFUSION EQUATION 646 10.5 INVERSION OF THE LAPLACE TRANSFORM 654 10.6 CONNECTION WITH RATIONAL APPROXIMATION 656 10.6.1 THE CARATHE ODORY-FEJ6R METHOD 663 10.7 PADE APPROXIMANTS FOR THE RICCATI EQUATION 670 11 CONNECTION WITH QUANTUM FIELD THEORY 674 11.1 PERTURBED HARMONIC OSCILLATORS 674 11.1.1 THE PERES MODEL 675 11.1.2 THE ANHARMONIC OSCILLATOR 678 11.2 PION-PION SCATTERING 679 11.3 LATTICE-CUTOFF K(^ N EUCLIDEAN FIELD THEORY, OR THE CONTINUOUS-SPIN ISING MODEL 684 APPENDIX: A FORTRAN FUNCTION 690 BIBH OGRAPHY 695 INDEX 741
any_adam_object	1
author	Baker, George A. 1932- Graves-Morris, Peter R.
author_GND	(DE-588)142605077 (DE-588)1145300251
author_facet	Baker, George A. 1932- Graves-Morris, Peter R.
author_role	aut aut
author_sort	Baker, George A. 1932-
author_variant	g a b ga gab p r g m prg prgm
building	Verbundindex
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classification_tum	MAT 415f
ctrlnum	(OCoLC)832312820 (DE-599)BVBBV010738963
dewey-full	515.2432
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	515 - Analysis
dewey-raw	515.2432
dewey-search	515.2432
dewey-sort	3515.2432
dewey-tens	510 - Mathematics
discipline	Mathematik
edition	2. ed.
format	Book
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indexdate	2024-07-09T17:58:03Z
institution	BVB
isbn	0521450071
language	English
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physical	XIV, 746 S. graph. Darst.
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series	Encyclopedia of mathematics and its applications
series2	Encyclopedia of mathematics and its applications
spelling	Baker, George A. 1932- Verfasser (DE-588)142605077 aut Padé approximants George A. Baker, Jr. ; Peter Graves-Morris 2. ed. Cambridge [u.a.] Cambridge Univ. Press 1996 XIV, 746 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 59 Padé-Näherung (DE-588)4173060-4 gnd rswk-swf Padé-Näherung (DE-588)4173060-4 s DE-604 Graves-Morris, Peter R. Verfasser (DE-588)1145300251 aut Encyclopedia of mathematics and its applications 59 (DE-604)BV000903719 59 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007170412&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Baker, George A. 1932- Graves-Morris, Peter R. Padé approximants Encyclopedia of mathematics and its applications Padé-Näherung (DE-588)4173060-4 gnd
subject_GND	(DE-588)4173060-4
title	Padé approximants
title_auth	Padé approximants
title_exact_search	Padé approximants
title_full	Padé approximants George A. Baker, Jr. ; Peter Graves-Morris
title_fullStr	Padé approximants George A. Baker, Jr. ; Peter Graves-Morris
title_full_unstemmed	Padé approximants George A. Baker, Jr. ; Peter Graves-Morris
title_short	Padé approximants
title_sort	pade approximants
topic	Padé-Näherung (DE-588)4173060-4 gnd
topic_facet	Padé-Näherung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007170412&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000903719
work_keys_str_mv	AT bakergeorgea padeapproximants AT gravesmorrispeterr padeapproximants

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