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Bibliographic Details
Main Authors:	Iserles, Arieh 1947- (Author), Nørsett, Syvert P. 1944-2024 (Author)
Format:	Book
Language:	English
Published:	London [u.a.] Chapman & Hall 1991
Edition:	1. ed.
Series:	Applied mathematics and mathematical computation 2
Subjects:	Approximation theory Differential equations > Numerical solutions Order stars (Mathematics) Padé-Näherungsbruch
Online Access:	Inhaltsverzeichnis
Physical Description:	XI, 248 S. graph. Darst.
ISBN:	0412352605

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MARC


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adam_text	Contents Preface viii 1 Introduction 1 2 General order stars 9 2.1 Order stars of the first kind 9 2.2 Essential singularities 16 2.3 Order stars of the second kind 22 3 Rational approximants to the exponential 28 3.1 Introduction 28 3.2 Collocation 29 3.3 Obrechkoff methods 32 3.4 Examples of approximants 35 3.5 Order barriers 41 3.6 Degree of real interpolation 42 3.7 Symmetric approximants with real poles 45 4 A acceptability barriers 50 4.1 Motivation 50 4.2 Maximal approximants 51 4.3 Hairer's representation of rational approximants 57 4.4 Restricted approximants 63 4.5 Interpolation with p restricted approximants 71 4.6 Complex fitting 76 5 Multistep methods 92 5.1 The first Dahlquist barrier 92 5.2 Order stars on Riemann surfaces 103 vi CONTENTS 5.3 The Daniel Moore conjecture and its solution 112 5.4 The Jeltsch Nevanlinna comparison theorem 116 6 The advection equation 120 6.1 Order and stability conditions 120 6.2 The influence of boundaries on stability 129 6.3 A barrier for semi discretizations 133 6.4 Stable full discretizations 141 6.5 A barrier for full discretizations 148 7 The diffusion equation 155 7.1 Methods of optimal order 155 7.2 Pade approximants to /((log z)2) 161 7.3 The order of optimal methods 163 7.4 Stability of optimal methods 171 8 Pade approximants 177 8.1 Block numbers of Pade tableaux 177 8.2 Nonvanishing functions 181 8.3 Functions with an infinite number of zeros 185 9 Contractive approximation 193 9.1 Zeros and contractions 193 9.2 The Pick Nevanlinna interpolation problem 202 10 Open problems 207 Problem 1 /4(a) acceptability of Pade approximants to exp z 208 Problem 2 Restricted Pade approximants to exp z 209 Problem 3 Polynomial aproximants to exp z 211 Problem 4 Multipoint Pade approximants to exp z 212 Problem 5 Multipoint restricted Pade approximants to exp z 214 Problem 6 The root condition for BDF 215 Problem 7 The root condition for general algebraic functions 217 Problem 8 Jeltsch Nevanlinna comparison theorems 218 Problem 9 Order reduction for Runge Kutta methods 218 Problem 10 Multistep methods for the advection equation 221 CONTENTS vii Problem 11 Advection equation with two space variables 224 Problem 12 Pade approximants to slit functions 225 Problem 13 Complex approximation and interpolation 226 Bibliography 228 Name index 239 Subject index 242
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discipline	Mathematik
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indexdate	2024-09-06T00:29:07Z
institution	BVB
isbn	0412352605
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-002915235
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physical	XI, 248 S. graph. Darst.
publishDate	1991
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publisher	Chapman & Hall
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series	Applied mathematics and mathematical computation
series2	Applied mathematics and mathematical computation
spelling	Iserles, Arieh 1947- Verfasser (DE-588)172163641 aut Order stars A. Iserles and S. P. Nørsett 1. ed. London [u.a.] Chapman & Hall 1991 XI, 248 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematics and mathematical computation 2 Approximation theory Differential equations Numerical solutions Order stars (Mathematics) Padé-Näherungsbruch (DE-588)4173061-6 gnd rswk-swf Padé-Näherungsbruch (DE-588)4173061-6 s DE-604 Nørsett, Syvert P. 1944-2024 Verfasser (DE-588)13758718X aut Applied mathematics and mathematical computation 2 (DE-604)BV006188231 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002915235&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Iserles, Arieh 1947- Nørsett, Syvert P. 1944-2024 Order stars Applied mathematics and mathematical computation Approximation theory Differential equations Numerical solutions Order stars (Mathematics) Padé-Näherungsbruch (DE-588)4173061-6 gnd
subject_GND	(DE-588)4173061-6
title	Order stars
title_auth	Order stars
title_exact_search	Order stars
title_full	Order stars A. Iserles and S. P. Nørsett
title_fullStr	Order stars A. Iserles and S. P. Nørsett
title_full_unstemmed	Order stars A. Iserles and S. P. Nørsett
title_short	Order stars
title_sort	order stars
topic	Approximation theory Differential equations Numerical solutions Order stars (Mathematics) Padé-Näherungsbruch (DE-588)4173061-6 gnd
topic_facet	Approximation theory Differential equations Numerical solutions Order stars (Mathematics) Padé-Näherungsbruch
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