Methods of shape-preserving spline approximation:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2000
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 338 S. |
| ISBN: | 9810240104 |
Internformat
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| 100 | 1 | |a Kvasov, Boris I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Methods of shape-preserving spline approximation |c Boris I. Kvasov |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2000 | |
| 300 | |a XVI, 338 S. | ||
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| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Curves |x Computer simulation | |
| 650 | 4 | |a Spline theory | |
| 650 | 4 | |a Surfaces |x Computer simulation | |
| 650 | 0 | 7 | |a Spline-Approximation |0 (DE-588)4182394-1 |2 gnd |9 rswk-swf |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010051883 | |
Datensatz im Suchindex
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/SK 470 K97 |
| DE-BY-FWS_katkey | 575923 |
| DE-BY-FWS_media_number | 083000513910 |
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| adam_text |
IMAGE 1
ETNODS OJ --
SHAPE-PRESERVING SPLINE APPROXIMATION
BORIS I. KVASOV RUSSIAN ACADEMY OF SCIENCES
IQ WORLD SCIENTIFIC !* SINGAPORE * NEW JERSEY * LONDON * HONG KONG
IMAGE 2
CONTENTS
PREFACE IX
INTRODUCTION 1
CHAPTER 1. INTERPOLATION BY POLYNOMIALS AND LAGRANGE SPLINES 7
1.1 POLYNOMIAL INTERPOLATION PROBLEM 7
1.2 LAGRANGE INTERPOLATION FORMULA 8
1.3 NEWTON INTERPOLATING POLYNOMIAL 11
1.4 GENERALIZED HORNER'S RULE 14
1.5 CONVERGENCE OFTHE INTERPOLATING POLYNOMIALS 18
1.6 PIECEWISE LINEAR INTERPOLATION 20
1.7 INTERPOLATION BY CUBIC LAGRANGE SPLINES 23
1.8 LOCAL APPROXIMATION BY CUBIC LAGRANGE SPLINES 26
1.9 LOCAL APPROXIMATION BY CUBIC B-SPLINES 28
1.10 INTERPOLATION BY QUADRATIC LAGRANGE SPLINES 30
1.11 LOCAL APPROXIMATION BY QUADRATIC LAGRANGE SPLINES 32
1.12 PROBLEMS 33
CHAPTER 2. CUBIC SPLINE INTERPOLATION 37
2.1 CUBIC INTERPOLATING SPLINES 37
2.2 DEFINING RELATIONS FOR CUBIC INTERPOLATING SPLINES 39
2.3 ENDPOINT CONSTRAINTS AND SYSTEMS OF LINEAR EQUATIONS . . . 40
2.4 DIAGONALLY DOMINANT MATRICES. EXISTENCE AND UNIQUENESS OF THE
SOLUTION 42
2.5 GAUSSIAN ELIMINATION FOR TRIDIAGONAL SYSTEMS 44
2.6 CORRECTNESS AND STABILITY OF GAUSSIAN ELIMINATION 45
2.7 FRONT GAUSSIAN ELIMINATION 46
2.8 EXAMPLE OF A CUBIC INTERPOLATING SPLINE 48
2.9 PERIODIC GAUSSIAN ELIMINATION 50
2.10 CORRECTNESS AND STABILITY OF PERIODIC GAUSSIAN ELIMINATION . . 53
2.11 FIRST DERIVATIVE ALGORITHM 54
2.12 AN EXAMPLE OF FIRST DERIVATIVE ALGORITHM 56
2.13 PROBLEMS 57
XIII
IMAGE 3
XIV METHODS OF SHAPE PRESERVING SPLINE APPROXIMATION
CHAPTER 3. ALGORITHMS FOR COMPUTING 1-D AND 2-D
POLYNOMIAL SPLINES , 61
3.1 DEFINITION OF SPLINES. THE SPACE OF SPLINES 61
3.2 BASIS SPLINES WITH FINITE SUPPORT 64
3.3 NORMALIZED BASIS SPLINES. REPRESENTATION OF POLYNOMIALS AND
TRUNCATED POWER FUNCTIONS 71
3.4 COMPUTING SPLINES AND THEIR DERIVATIVES 77
3.5 CARDINAL SPLINES. LAGRANGE AND HERMITE INTERPOLATION FORMULAE FOR
SPLINES 83
3.6 EXTREMAL PROPERTIES OF EVEN ORDER POLYNOMIAL SPLINES 88
3.7 SPLINE FUNCTIONS OF TWO VARIABLES ON A RECTANGULAR MESH . . 91
CHAPTER 4. METHODS OF MONOTONE AND CONVEX SPLINE INTERPOLATION 97
4.1 INTRODUCTION 97
4.2 MONOTONICITY PRESERVING INTERPOLATION BY C 1 CUBIC SPLINES . . . 102
4.3 MONOTONE AND CONVEX INTERPOLATION BY C 2 CUBIC SPLINES . . . 107
4.3.1 MONOTONE MATRICES. LEMMA ON TRIDIAGONAL SYSTEM 107
4.3.2 CONVEX CUBIC SPLINES 109
4.3.3 MONOTONE CUBIC SPLINES 111
4.4 MONOTONE AND CONVEX INTERPOLATION BY GENERALIZED TENSION SPLINES 113
4.4.1 GENERALIZED TENSION SPLINES. CONDITIONS OF EXISTENCE AND
UNIQUENESS 113
4.4.2 CONVEX INTERPOLATION BY GENERALIZED TENSION SPLINES 117
4.4.3 MONOTONE INTERPOLATION BY GENERALIZED TENSION SPLINES . . 119
4.4.4 NECESSARY AND SUMCIENT CONDITIONS FOR MONOTONICITY OF GENERALIZED
TENSION SPLINES 121
4.4.5 CHOICE OF DEFINING FUNCTIONS AND TENSION PARAMETERS . . . 123
4.5 HISTORICAL NOTES 126
CHAPTER 5. METHODS OF SHAPE-PRESERVING SPLINE INTERPOLATION 127
5.1 A CLASS OF SHAPE-PRESERVING FUNCTIONS 127
5.2 CLASSIFICATION OF THE DATA 128
5.3 SOLUTION OF THE HERMITE INTERPOLATION PROBLEM WITH CONSTRAINTS . 134
5.4 NUMERICAL ALGORITHM FOR CONSTRUCTING A SHAPE-PRESERVING FUNCTION 141
5.5 SOFTWARE IMPLEMENTATION OF THE ALGORITHM 146
5.6 GRAPHICAL EXAMPLES 149
IMAGE 4
CONTENTS XV
CHAPTER 6. LOCAL BASES FOR GENERALIZED TENSION SPLINES . . . 153
6.1 GENERALIZED TENSION SPLINES. CONDITIONS OF EXISTENCE AND UNIQUENESS
153
6.2 CONSTRUCTION OF GB-SPLINES 157
6.3 A SECOND METHOD FOR CONSTRUCTING GB-SPLINES 159
6.4 DEFINITION OF GB-SPLINES THROUGH DIFFERENCES 162
6.5 RECURRENCE FORMULAE FOR GB-SPLINES 163
6.6 PROPERTIES OF GB-SPLINES 164
6.7 SERIES OF GB-SPLINES 168
6.8 TRANSFORMATIONS BETWEEN SPLINE REPRESENTATIONS 174
6.9 FORMULAE FOR LOCAL APPROXIMATION BY GB-SPLINES 176
6.10 EXAMPLES OF GB-SPLINES 178
6.10.1 PARABOLIC GB-SPLINES 180
CHAPTER 7. GB-SPLINES OF ARBITRARY ORDER 183
7.1 GB-SPLINES OF ARBITRARY ORDER 183
7.2 RECURSIVE ALGORITHM FOR THE CALCULATION OF GB-SPLINES 186
7.3 ANOTHER REPRESENTATION FOR GB-SPLINES 194
7.4 PROPERTIES OF GB-SPLINES 196
7.5 SERIES OF GB-SPLINES . 2 01
7.6 INVARIANCE OF GENERALIZED SPLINES WITH RESPECT TO AFFINE
TRANSFORMATIONS 206
7.7 LOCAL APPROXIMATION BY GB-SPLINES 208
7.8 EXAMPLES 211
CHAPTER 8. METHODS OF SHAPE PRESERVING LOCAL SPLINE APPROXIMATION 213
8.1 THE PROBLEM OF SHAPE PRESERVING APPROXIMATION 214
8.2 A ONE-POINT ALGORITHM FOR SHAPE PRESERVING APPROXIMATION . . 216 8.3
A THREE-POINT ALGORITHM FOR SHAPE PRESERVING APPROXIMATION . 221 8.4
SHAPE PRESERVING SURFACE APPROXIMATION 225
8.5 GRAPHICAL EXAMPLES . 228
CHAPTER 9. DIFFERENCE METHOD FOR CONSTRUCTION HYPERBOLIC TENSION SPLINES
237
9.1 FINITE DIFFERENCE APPROXIMATION 238
9.2 SYSTEM SPLITTING AND MESH SOLUTION EXTENSION 239
9.3 ERROR ESTIMATES 242
9.4 DISCRETE HYPERBOLIC TENSION B-SPLINES 245
9.4.1 CONSTRUCTION OF DISCRETE HB-SPLINES 246
IMAGE 5
XVI METHODS OF SHAPE PRESERVING SPLINE APPROXIMATION
9.4.2 RECURRENCE FORMULAE FOR DISCRETE HB-SPLINES 248
9.4.3 FORMULAE FOR LOCAL APPROXIMATION BY DISCRETE HB-SPLINES . . 251
9.5 COMPUTATIONAL ASPECTS 253
9.5.1 THE PENTADIAGONAL SYSTEM 254
9.5.2 THE UNIFORM GASE 255
9.5.3 SYSTEM SPLITTING 257
9.6 GRAPHICAL EXAMPLES 259
CHAPTER 10. DISCRETE GENERALIZED TENSION SPLINES 263
10.1 DISCRETE GENERALIZED SPLINES. CONDITIONS OF EXISTENCE AND
UNIQUENESS 263
10.2 CONSTRUCTION OF BASIS SPLINES 268
10.3 PROPERTIES OF DISCRETE GB-SPLINES 271
10.4 DEFINITION OF DISCRETE GB-SPLINES THROUGH DIFFERENCES 273
10.5 TRANSFORMATIONS BETWEEN SPLINE REPRESENTATIONS 274
10.6 LOCAL APPROXIMATION BY DISCRETE GB-SPLINE 275
10.7 THE CASE OF DISCRETE CUBIC SPLINES 277
10.7.1 PIECEWISE CUBIC LAGRANGE POLYNOMIAL 279
10.8 RECURRENCE FORMULAE FOR DISCRETE GB-SPLINES 279
10.8.1 THE UNIFORM CASE 281
10.9 SERIES OF DISCRETE GB-SPLINES 283
10.10 EXAMPLES OF DEFINING FUNCTIONS 288
10.11 HISTORICAL NOTES . 2 89
CHAPTER 11. M E T H O DS OF SHAPE PRESERVING PARAMETRIZATION 291
11.1 GENERAL CONSIDERATION 291
11.2 AFFINE INVARIANCE OF POLYNOMIALS AND SPLINES 293
11.3 MONOTONICITY PRESERVING PARAMETRIZATION 295
11.4 PARAMETRIZATION FOR CUBIC SPLINES 298
11.5 PARAMETRIZATION UNDER SURFACE CONSTRUCTION 301
11.6 GRAPHICAL EXAMPLES 303
REFERENCES 309
APPENDIX A. EXAMPLE: RECONSTRUCTION OF A SHIP SURFACE 323
APPENDIX B. COMPUTER PROGRAMS FOR SHAPE PRESERVING SURFACE APPROXIMATION
329
INDEX 333 |
| any_adam_object | 1 |
| author | Kvasov, Boris I. |
| author_facet | Kvasov, Boris I. |
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| author_sort | Kvasov, Boris I. |
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| indexdate | 2025-01-28T11:12:13Z |
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| isbn | 9810240104 |
| language | English |
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| physical | XVI, 338 S. |
| publishDate | 2000 |
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| publisher | World Scientific |
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| spelling | Kvasov, Boris I. Verfasser aut Methods of shape-preserving spline approximation Boris I. Kvasov Singapore [u.a.] World Scientific 2000 XVI, 338 S. txt rdacontent n rdamedia nc rdacarrier Approximation theory Curves Computer simulation Spline theory Surfaces Computer simulation Spline-Approximation (DE-588)4182394-1 gnd rswk-swf Spline-Approximation (DE-588)4182394-1 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010051883&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kvasov, Boris I. Methods of shape-preserving spline approximation Approximation theory Curves Computer simulation Spline theory Surfaces Computer simulation Spline-Approximation (DE-588)4182394-1 gnd |
| subject_GND | (DE-588)4182394-1 |
| title | Methods of shape-preserving spline approximation |
| title_auth | Methods of shape-preserving spline approximation |
| title_exact_search | Methods of shape-preserving spline approximation |
| title_full | Methods of shape-preserving spline approximation Boris I. Kvasov |
| title_fullStr | Methods of shape-preserving spline approximation Boris I. Kvasov |
| title_full_unstemmed | Methods of shape-preserving spline approximation Boris I. Kvasov |
| title_short | Methods of shape-preserving spline approximation |
| title_sort | methods of shape preserving spline approximation |
| topic | Approximation theory Curves Computer simulation Spline theory Surfaces Computer simulation Spline-Approximation (DE-588)4182394-1 gnd |
| topic_facet | Approximation theory Curves Computer simulation Spline theory Surfaces Computer simulation Spline-Approximation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010051883&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kvasovborisi methodsofshapepreservingsplineapproximation |
Inhaltsverzeichnis
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