Padé approximants:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1996
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
59 |
| Schlagwörter: | |
| Links: | 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 |
| Umfang: | XIV, 746 S. graph. Darst. |
| ISBN: | 0521450071 |
Internformat
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0001 96 A 3463 |
|---|---|
| DE-BY-TUM_katkey | 780950 |
| DE-BY-TUM_location | Mag |
| DE-BY-TUM_media_number | 040001112958 |
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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 |
| bvnumber | BV010738963 |
| classification_rvk | SK 470 |
| 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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| id | DE-604.BV010738963 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:59:47Z |
| institution | BVB |
| isbn | 0521450071 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007170412 |
| oclc_num | 832312820 |
| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM DE-703 DE-11 DE-188 |
| owner_facet | DE-12 DE-91 DE-BY-TUM DE-703 DE-11 DE-188 |
| physical | XIV, 746 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| 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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Bibliotheksmagazin
| Signatur: |
0001 96 A 3463 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |