Multidimensional minimizing splines: theory and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Kluwer Acad. Publ.
2004
|
| Series: | Grenoble sciences
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. [247]-256) and index |
| Physical Description: | XV, 261 S. graph. Darst. 24 cm |
| ISBN: | 1402077866 |
Staff View
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| 264 | 1 | |a Boston [u.a.] |b Kluwer Acad. Publ. |c 2004 | |
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Record in the Search Index
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| adam_text | MULTIDIMENSIONAL MINIMIZING SPLINES THEORY AND APPLICATIONS BY REMI
ARCANGELI MARIA CRUZ L6PEZ DE SILANES JUAN JOSE TORRENS KLUWER ACADEMIC
PUBLISHERS BOSTON / DORDRECHT / NEW YORK / LONDON CONTENTS PREFACE IX
PRELIMINARIES XIII PART A. (RA, S)-SPLINES 1 INTRODUCTION 3 I. THE
SPACES X M S 5 1. DEFINITION 5 2. IMBEDDINGS AND NORMS 7 II.
INTERPOLATING (M, S)-SPLINES 13 1. DEFINITION AND FIRST PROPERTIES 13 2.
THE SPACE OF (M, S)-SPLINE FUNCTIONS. EXAMPLES 15 3. OTHER PROBLEMS.
SPLINES DENNED BY LOCAL MEAN VALUES 22 4. COMPUTATION OF INTERPOLATING
SPLINES 25 5. A CONVERGENCE RESULT 27 6. AUXILIARY RESULTS 31 7.
ESTIMATES OF THE APPROXIMATION ERROR 35 III. SMOOTHING (M, S)-SPLINES 39
1. DEFINITION AND FIRST PROPERTIES 39 2. COMPUTATION OF SMOOTHING
SPLINES . 40 3. CONVERGENCE RESULTS 42 4. ESTIMATES OF THE APPROXIMATION
ERROR 46 5. CONVERGENCE FOR NOISY DATA 50 IV. (M, J, S)-SPLINES 53 1.
THE SPACES X M ^ A 53 2. INTERPOLATING (RA,Z,S)-SPLINES 54 VI
MULTIDIMENSIONAL MINIMIZING SPLINES 3. SMOOTHING (M, Z,S)-SPLINES 55
PART B. M -SPLINES OVER A BOUNDED DOMAIN OF R N 57 INTRODUCTION 59 V.
M -SPLINES OVER O 61 1. INTERPOLATING J D TN -SPLINES 61 2. THE SPACE
OF M -SPLINES 64 3. SMOOTHING _D M -SPLINES 65 4. CONVERGENCE AND
ERROR ESTIMATES 66 VI. DISCRETE M -SPLINES 69 1. THE FINITE ELEMENT
FRAMEWORK 69 2. DISCRETE INTERPOLATING D M -SPLINES . 72 2.1. DEFINITION
AND PROPERTIES 72 2.2. CONVERGENCE AND ERROR ESTIMATES 74 3. DISCRETE
SMOOTHING D M -SPLINES 80 3.1. DEFINITION AND PROPERTIES 80 3.2.
CONVERGENCE AND ERROR ESTIMATES 82 VII. UNIVARIATE M -SPLINES 89 1.
CHARACTERIZATION AND EXPLICIT FORM 89 2. COMPUTATION OF Z) M -SPLINES .
93 3. CUBIC SPLINES 95 3.1. NATURAL CUBIC SPLINES 96 3.2. CLAMPED CUBIC
SPLINES 97 3.3. THE BASIS OF CUBIC JB-SPLINES 98 4. TENSOR PRODUCT OF
UNIVARIATE -D M -SPLINES 99 PART C. APPLICATIONS OF DISCRETE D M
-SPLINES . 101 INTRODUCTION 103 CONTENTS VII VIII. CONSTRUCTION OF
EXPLICIT SURFACES FROM LARGE DATA SETS 105 1. FORMULATION OF THE PROBLEM
105 2. THE FITTING METHOD 105 3. EXAMPLES OF FINITE ELEMENTS 107 4.
CONVERGENCE RESULTS 110 5. AN INTERPOLATION-SMOOTHING MIXED METHOD 110
6. NUMERICAL RESULTS 113 IX. APPROXIMATION OF FAULTED EXPLICIT SURFACES
131 1. FORMULATION OF THE PROBLEM 131 2. SPACES OF FUNCTIONS ON Q 133
2.1. DEFINITION OF THE DISCONTINUITY SET F 133 2.2. SPACES C^(Q ), H M
(N ) AND H M {N F ) DC R (TT) 134 3. M -SPLINES OVER W 136 4.
DISCRETE D M -SPLINES 140 5. GLOBAL CONVERGENCE 145 6. LOCAL CONVERGENCE
148 7. APPROXIMATION OF EXPLICIT SURFACES WITH VERTICAL FAULTS 157 8.
NUMERICAL RESULTS 160 X. FITTING AN EXPLICIT SURFACE ALONG A SET OF
CURVES 175 1. FORMULATION OF THE PROBLEM 175 2. APPROXIMATION OF || *
||Q P 177 3. SPLINE FITTING 179 4. CONVERGENCE OF THE APPROXIMATION 183
5. NUMERICAL RESULTS 188 XI. FITTING AN EXPLICIT SURFACE OVER AN OPEN
SET 199 1. FORMULATION OF THE PROBLEM 199 2. SPLINE FITTING 199 3.
CONVERGENCE OF THE APPROXIMATION 204 4. NUMERICAL RESULTS 208 VIII
MULTIDIMENSIONAL MINIMIZING SPLINES XII. APPROXIMATION OF PARAMETRIC
SURFACES 219 1. INTRODUCTION 219 2. FORMULATION OF THE PROBLEM 220 3.
SPLINE FITTING 222 4. CONVERGENCE OF THE APPROXIMATION 225 5. NUMERICAL
RESULTS 227 BIBLIOGRAPHY 247 INDEX 257
|
| adam_txt |
MULTIDIMENSIONAL MINIMIZING SPLINES THEORY AND APPLICATIONS BY REMI
ARCANGELI MARIA CRUZ L6PEZ DE SILANES JUAN JOSE TORRENS KLUWER ACADEMIC
PUBLISHERS BOSTON / DORDRECHT / NEW YORK / LONDON CONTENTS PREFACE IX
PRELIMINARIES XIII PART A. (RA, S)-SPLINES 1 INTRODUCTION 3 I. THE
SPACES X M ' S 5 1. DEFINITION 5 2. IMBEDDINGS AND NORMS 7 II.
INTERPOLATING (M, S)-SPLINES 13 1. DEFINITION AND FIRST PROPERTIES 13 2.
THE SPACE OF (M, S)-SPLINE FUNCTIONS. EXAMPLES 15 3. OTHER PROBLEMS.
SPLINES DENNED BY LOCAL MEAN VALUES 22 4. COMPUTATION OF INTERPOLATING
SPLINES 25 5. A CONVERGENCE RESULT 27 6. AUXILIARY RESULTS 31 7.
ESTIMATES OF THE APPROXIMATION ERROR 35 III. SMOOTHING (M, S)-SPLINES 39
1. DEFINITION AND FIRST PROPERTIES 39 2. COMPUTATION OF SMOOTHING
SPLINES . 40 3. CONVERGENCE RESULTS 42 4. ESTIMATES OF THE APPROXIMATION
ERROR 46 5. CONVERGENCE FOR NOISY DATA 50 IV. (M, J, S)-SPLINES 53 1.
THE SPACES X M ^ A 53 2. INTERPOLATING (RA,Z,S)-SPLINES 54 VI
MULTIDIMENSIONAL MINIMIZING SPLINES 3. SMOOTHING (M, Z,S)-SPLINES 55
PART B. M -SPLINES OVER A BOUNDED DOMAIN OF R N 57 INTRODUCTION 59 V.
M -SPLINES OVER O 61 1. INTERPOLATING J D TN -SPLINES 61 2. THE SPACE
OF M -SPLINES 64 3. SMOOTHING _D M -SPLINES 65 4. CONVERGENCE AND
ERROR ESTIMATES 66 VI. DISCRETE M -SPLINES 69 1. THE FINITE ELEMENT
FRAMEWORK 69 2. DISCRETE INTERPOLATING D M -SPLINES . 72 2.1. DEFINITION
AND PROPERTIES 72 2.2. CONVERGENCE AND ERROR ESTIMATES 74 3. DISCRETE
SMOOTHING D M -SPLINES 80 3.1. DEFINITION AND PROPERTIES 80 3.2.
CONVERGENCE AND ERROR ESTIMATES 82 VII. UNIVARIATE M -SPLINES 89 1.
CHARACTERIZATION AND EXPLICIT FORM 89 2. COMPUTATION OF Z) M -SPLINES .
93 3. CUBIC SPLINES 95 3.1. NATURAL CUBIC SPLINES 96 3.2. CLAMPED CUBIC
SPLINES 97 3.3. THE BASIS OF CUBIC JB-SPLINES 98 4. TENSOR PRODUCT OF
UNIVARIATE -D M -SPLINES 99 PART C. APPLICATIONS OF DISCRETE D M
-SPLINES . 101 INTRODUCTION 103 CONTENTS VII VIII. CONSTRUCTION OF
EXPLICIT SURFACES FROM LARGE DATA SETS 105 1. FORMULATION OF THE PROBLEM
105 2. THE FITTING METHOD 105 3. EXAMPLES OF FINITE ELEMENTS 107 4.
CONVERGENCE RESULTS 110 5. AN INTERPOLATION-SMOOTHING MIXED METHOD 110
6. NUMERICAL RESULTS 113 IX. APPROXIMATION OF FAULTED EXPLICIT SURFACES
131 1. FORMULATION OF THE PROBLEM 131 2. SPACES OF FUNCTIONS ON Q' 133
2.1. DEFINITION OF THE DISCONTINUITY SET F 133 2.2. SPACES C^(Q'), H M
(N') AND H M {N F ) DC R (TT) 134 3. M -SPLINES OVER W 136 4.
DISCRETE D M -SPLINES 140 5. GLOBAL CONVERGENCE 145 6. LOCAL CONVERGENCE
148 7. APPROXIMATION OF EXPLICIT SURFACES WITH VERTICAL FAULTS 157 8.
NUMERICAL RESULTS 160 X. FITTING AN EXPLICIT SURFACE ALONG A SET OF
CURVES 175 1. FORMULATION OF THE PROBLEM 175 2. APPROXIMATION OF || *
||Q P 177 3. SPLINE FITTING 179 4. CONVERGENCE OF THE APPROXIMATION 183
5. NUMERICAL RESULTS 188 XI. FITTING AN EXPLICIT SURFACE OVER AN OPEN
SET 199 1. FORMULATION OF THE PROBLEM 199 2. SPLINE FITTING 199 3.
CONVERGENCE OF THE APPROXIMATION 204 4. NUMERICAL RESULTS 208 VIII
MULTIDIMENSIONAL MINIMIZING SPLINES XII. APPROXIMATION OF PARAMETRIC
SURFACES 219 1. INTRODUCTION 219 2. FORMULATION OF THE PROBLEM 220 3.
SPLINE FITTING 222 4. CONVERGENCE OF THE APPROXIMATION 225 5. NUMERICAL
RESULTS 227 BIBLIOGRAPHY 247 INDEX 257 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T16:28:15Z |
| indexdate | 2024-07-09T20:52:37Z |
| institution | BVB |
| isbn | 1402077866 |
| language | English |
| lccn | 2004051671 |
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| physical | XV, 261 S. graph. Darst. 24 cm |
| publishDate | 2004 |
| publishDateSearch | 2004 |
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| publisher | Kluwer Acad. Publ. |
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| series2 | Grenoble sciences |
| spelling | Arcangéli, Rémi Verfasser aut Multidimensional minimizing splines theory and applications by Rémi Arcangéli ; María Cruz López de Silanes ; Juan José Torrens Boston [u.a.] Kluwer Acad. Publ. 2004 XV, 261 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Grenoble sciences Includes bibliographical references (p. [247]-256) and index Approximation, Théorie de l' Splines, Théorie des aSpline theory aApproximation theory Spline-Approximation (DE-588)4182394-1 gnd rswk-swf Spline-Approximation (DE-588)4182394-1 s DE-604 López de Silanes, Maria Cruz Sonstige oth Torrens, Juan José Sonstige oth HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015429581&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arcangéli, Rémi Multidimensional minimizing splines theory and applications Approximation, Théorie de l' Splines, Théorie des aSpline theory aApproximation theory Spline-Approximation (DE-588)4182394-1 gnd |
| subject_GND | (DE-588)4182394-1 |
| title | Multidimensional minimizing splines theory and applications |
| title_auth | Multidimensional minimizing splines theory and applications |
| title_exact_search | Multidimensional minimizing splines theory and applications |
| title_exact_search_txtP | Multidimensional minimizing splines theory and applications |
| title_full | Multidimensional minimizing splines theory and applications by Rémi Arcangéli ; María Cruz López de Silanes ; Juan José Torrens |
| title_fullStr | Multidimensional minimizing splines theory and applications by Rémi Arcangéli ; María Cruz López de Silanes ; Juan José Torrens |
| title_full_unstemmed | Multidimensional minimizing splines theory and applications by Rémi Arcangéli ; María Cruz López de Silanes ; Juan José Torrens |
| title_short | Multidimensional minimizing splines |
| title_sort | multidimensional minimizing splines theory and applications |
| title_sub | theory and applications |
| topic | Approximation, Théorie de l' Splines, Théorie des aSpline theory aApproximation theory Spline-Approximation (DE-588)4182394-1 gnd |
| topic_facet | Approximation, Théorie de l' Splines, Théorie des aSpline theory aApproximation theory Spline-Approximation |
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