Error inequalities in polynomial interpolation and their applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer
1993
|
| Schriftenreihe: | Mathematics and its applications
262 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 365 S. |
| ISBN: | 0792323378 |
Internformat
MARC
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| 245 | 1 | 0 | |a Error inequalities in polynomial interpolation and their applications |c by Ravi P. Agarwal and Patricia J. Y. Wong |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer |c 1993 | |
| 300 | |a X, 365 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Mathematics and its applications |v 262 | |
| 650 | 7 | |a Approximation, théorie de l' |2 ram | |
| 650 | 7 | |a Polynômes |2 ram | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Interpolation | |
| 650 | 4 | |a Polynomials | |
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| 689 | 0 | 1 | |a Fehlerabschätzung |0 (DE-588)4228085-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Wong, Patricia J. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804122535045890048 |
|---|---|
| adam_text | CONTENTS
Preface ix
Chapter 1 LIDSTONE INTERPOLATION
1.1 Introduction 1
1.2 Lidstone Polynomials 2
1.3 Interpolating Polynomial Representations 17
1.4 Error Representations 17
Peano s Representation 18
Cauchy s Representation 18
1.5 Error Estimates 19
1.6 Lidstone Boundary Value Problems 21
Existence and Uniqueness 21
Picard s and Approximate Picard s Iteration 29
Quasilinearization and Approximate Quasilinearization 43
References 59
Chapter 2 HERMITE INTERPOLATION
2.1 Introduction 62
2.2 Interpolating Polynomial Representations 63
Method of Lagrange 63
Method of Newton 67
2.3 Error Representations 71
Cauchy s Representation 71
Newton s Representation 72
Peano s Representation 73
A New Representation 77
vi
2.4 Error Estimates 91
Error Estimates in Interpolation 91
Error Estimates for Derivatives 105
2.5 Some Applications 149
Generalized Maximum Principle 149
Hermite Boundary Value Problems 151
Generalized Liapunoff s Inequality 161
Generalized Hartman s Inequality 162
A Lower Bound for the Zeros of the Solutions 164
A Test for Disconjugacy 166
References 168
Chapter 3 ABEL GONTSCHAROFF INTERPOLATION
3.1 Introduction 172
3.2 Interpolating Polynomial Representations 173
3.3 Error Representations 175
Repeated Integrals Representation 175
Peano s Representation 175
Cauchy s Representation 177
3.4 Error Estimates 178
3.5 Some Applications 186
References 189
Chapter 4 MISCELLANEOUS INTERPOLATION
4.1 Introduction 192
4.2 (n,p) and (p,n) Interpolation 192
4.3 (0,0;m,n m) Interpolation 198
4.4 (0; rn,n — m) Interpolation 203
4.5 (0,2,0; m, n m) Interpolation 206
4.6 (0 : I 1,1: / + j 1; m, n m) Interpolation 208
4.7 (0; Lidstone) Interpolation 209
vii
4.8 (0,2,0; Lidstone) Interpolation 210
4.9 (1,3,0,1; Lidstone) Interpolation 211
4.10 (0 : Z — 1,7: 1 + j 1; Lidstone) Interpolation 213
4.11 (0,2,1; Lidstone) Interpolation 214
References 216
Chapter 5 PIECEWISE POLYNOMIAL INTERPOLATION
5.1 Introduction 217
5.2 Preliminaries 218
5.3 Piecewise Hermite Interpolation 228
5.4 Piecewise Lidstone Interpolation 257
5.5 Two Variable Piecewise Hermite Interpolation 266
5.6 Two Variable Piecewise Lidstone Interpolation 274
References 278
Chapter 6 SPLINE INTERPOLATION
6.1 Introduction 281
6.2 Preliminaries 282
6.3 Cubic Spline Interpolation 285
6.4 Quintic Spline Interpolation : r = 4 290
6.5 Approximated Quintic Splines : r = 4 301
6.6 Quintic Spline Interpolation : r = 3 309
6.7 Approximated Quintic Splines : r = 3 315
6.8 Cubic Lidstone Spline Interpolation 321
6.9 Quintic Lidstone Spline Interpolation 323
6.10 L2 Error Bounds for Spline Interpolation 327
6.11 Two Variable Spline Interpolation 334
6.12 Two Variable Lidstone Spline Interpolation 346
6.13 Some Applications 350
Linear Integral Equations 351
References 360
Name Index 363
|
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| id | DE-604.BV008151611 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:15:25Z |
| institution | BVB |
| isbn | 0792323378 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005379061 |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Agarwal, Ravi P. 1947- Verfasser (DE-588)112040187 aut Error inequalities in polynomial interpolation and their applications by Ravi P. Agarwal and Patricia J. Y. Wong Dordrecht u.a. Kluwer 1993 X, 365 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 262 Approximation, théorie de l' ram Polynômes ram Approximation theory Interpolation Polynomials Polynom-Interpolationsverfahren (DE-588)4175264-8 gnd rswk-swf Fehlerabschätzung (DE-588)4228085-0 gnd rswk-swf Polynom-Interpolationsverfahren (DE-588)4175264-8 s Fehlerabschätzung (DE-588)4228085-0 s DE-604 Wong, Patricia J. Verfasser aut Mathematics and its applications 262 (DE-604)BV008163334 262 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005379061&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Agarwal, Ravi P. 1947- Wong, Patricia J. Error inequalities in polynomial interpolation and their applications Mathematics and its applications Approximation, théorie de l' ram Polynômes ram Approximation theory Interpolation Polynomials Polynom-Interpolationsverfahren (DE-588)4175264-8 gnd Fehlerabschätzung (DE-588)4228085-0 gnd |
| subject_GND | (DE-588)4175264-8 (DE-588)4228085-0 |
| title | Error inequalities in polynomial interpolation and their applications |
| title_auth | Error inequalities in polynomial interpolation and their applications |
| title_exact_search | Error inequalities in polynomial interpolation and their applications |
| title_full | Error inequalities in polynomial interpolation and their applications by Ravi P. Agarwal and Patricia J. Y. Wong |
| title_fullStr | Error inequalities in polynomial interpolation and their applications by Ravi P. Agarwal and Patricia J. Y. Wong |
| title_full_unstemmed | Error inequalities in polynomial interpolation and their applications by Ravi P. Agarwal and Patricia J. Y. Wong |
| title_short | Error inequalities in polynomial interpolation and their applications |
| title_sort | error inequalities in polynomial interpolation and their applications |
| topic | Approximation, théorie de l' ram Polynômes ram Approximation theory Interpolation Polynomials Polynom-Interpolationsverfahren (DE-588)4175264-8 gnd Fehlerabschätzung (DE-588)4228085-0 gnd |
| topic_facet | Approximation, théorie de l' Polynômes Approximation theory Interpolation Polynomials Polynom-Interpolationsverfahren Fehlerabschätzung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005379061&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
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