Spline functions and multivariate interpolations:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1993
|
| Series: | Mathematics and its applications
248 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 265 - 272 |
| Physical Description: | IX, 276 S. graph. Darst. |
| ISBN: | 0792322290 |
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Record in the Search Index
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| adam_text | IMAGE 1
SPLINE FUNCTIONS AND
MULTIVARIATE INTERPOLATIONS
BY B. D. BOJANOV
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF SOFIA, SOFIA, BULGARIA
H. A. HAKOPIAN
DEPARTMENT OF MATHEMATICS, YEREVAN UNIVERSITY, YEREVAN, ARMENIA
AND
A. A. SAHAKIAN
DEPARTMENT OF MATHEMATICS, YEREVAN UNIVERSITY, YEREVAN, ARMENIA
KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
IMAGE 2
CONTENTS
PREFACE IX
CHAPTER 1. INTERPOLATION BY ALGEBRAIC POLYNOMIALS 1
1.1. LAGRANGE INTERPOLATION FORMULA 1
1.2. THE HERMITE INTERPOLATION PROBLEM 2
1.3. DIVIDED DIFFERENCES 4
1.4. BIRKHOFF INTERPOLATION 12
1.5. BUDAN-FOURIER THEOREM 14
NOTES AND REFERENCES 18
CHAPTER 2. THE SPACE OF SPLINES 19
2.1. POLYNOMIAL SPLINE FUNCTIONS 19
2.2. THE CLOSURE OF THE SPLINE SPACE 21
2.3. SPLINES WITH MULTIPLE KNOTS 25
NOTES AND REFERENCES 27
CHAPTER 3. SS-SPLINES 28
3.1. PEANO S KERNEL 28
3.2. DEFINITION OF 5-SPLINES 29
3.3. 5-SPLINE BASIS 33
3.4. RECURRENCE RELATIONS 36
3.4.1. THE BASIC RECURRENCE RELATION 36
3.4.2. DIFFERENTIATION OF SPLINES 38
3.4.3. TSCHAKALOFF S FORMULA 39
3.5. VARIATION DIMINISHING PROPERTY 41
NOTES AND REFERENCES 43
CHAPTER 4. INTERPOLATION BY SPLINE FUNCTIONS 45
4.1. TOTAL POSITIVITY 45
4.2. HERMITE INTERPOLATION 49
4.3. BIRKHOFF INTERPOLATION 52
4.3.1. 5-SPLINES WITH BIRKHOFF S KNOTS 53
4.3.2. SIGN CHANGES OF A SPLINE FUNCTION 60
4.3.3. MAIN INTERPOLATION THEOREM 60
4.4. TOTAL POSITIVITY OF THE TRUNCATED POWER KERNEL 63
NOTES AND REFERENCES 66
IMAGE 3
VI
CONTENTS
CHAPTER 5. NATURAL SPLINE FUNCTIONS 67
5.1. INTERPOLATION BY NATURAL SPLINE FUNCTIONS 67
5.1.1. DEFINITION 67
5.1.2. INTERPOLATION 68
5.1.3. HOLLADAY S THEOREM 72
5.2. BEST APPROXIMATION OF LINEAR FUNCTIONALS 75
5.3. EXTREMAL PROPERTY OF THE NATURAL SPLINE INTERPOLATION 78
NOTES AND REFERENCES 81
CHAPTER 6. PERFECT SPLINES 6.1. FAVARD S INTERPOLATION PROBLEM 6.2.
OSCILLATING PERFECT SPLINES 6.2.1. SPLINES WITH PREASSIGNED INTEGRALS
OVER SUBINTERVALS
6.2.2. INTERPOLATION AT THE EXTREMAL POINTS 6.2.3. PERFECT SPLINES OF
LEAST UNIFORM NORM 6.3. OPTIMAL RECOVERY OF FUNCTIONS 6.3.1. THE BEST
METHOD OF RECOVERY
6.3.2. CHARACTERIZATION OF THE OPTIMAL NODES 6.4. SMOOTHEST INTERPOLANT
NOTES AND REFERENCES
CHAPTER 7. MONOSPLINES 7.1. MONOSPLINES AND QUADRATURE FORMULAE 7.2.
ZEROS OF MONOSPLINES 7.3. THE FUNDAMENTAL THEOREM OF ALGEBRA FOR
MONOSPLINES
NOTES AND REFERENCES
CHAPTER 8. PERIODIC SPLINES 8.1. BASIS
8.1.1. PERIODIC OE-SPLINES 8.1.2. REPRESENTATION BY THE BERNOULLI
POLYNOMIALS 8.2. HERMITE INTERPOLATION 8.3. FAVARD S PROBLEM
NOTES AND REFERENCES
CHAPTER 9. MULTIVARIATE SS-SPLINES AND TRUNCATED POWERS 9.1. A GEOMETRIE
INTERPRETATION OF UNIVARIATE S-SPLINES AND TRUNCATED POWERS 9.2.
MULTIVARIATE 5-SPLINES AND TRUNCATED POWERS 9.3. RECURRENCE RELATIONS
FOR 5-SPLINES 9.4. RIDGE FUNCTIONS
NOTES AND REFERENCES
CHAPTER 10. MULTIVARIATE SPLINE FUNCTIONS AND DIVIDED DIFFERENCES 10.1.
MULTIVARIATE SPLINE FUNCTIONS
IMAGE 4
VII
10.2. MULTIVARIATE DIVIDED DIFFERENCES 156
10.3. POLYHEDRAL SPLINES 159
NOTES AND REFERENCES 162
CHAPTER 11. BOX SPLINES 163
11.1. DEFINITION AND BASIC PROPERTIES 163
11.2. INTEGER TRANSLATES OF A BOX SPLINE 168
11.3. A SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS CONNECTED WITH V(X) 172
11.4. FURTHER PROPERTIES OF THE SPACES V(X) AND V(X) 175
11.5. LINEAR INDEPENDENCE OF TRANSLATES OF A BOX SPLINE 188
11.6. INTERPOLATION BY TRANSLATES OF A BOX SPLINE 192
NOTES AND REFERENCES 196
CHAPTER 12. MULTIVARIATE MEAN VALUE INTERPOLATION 198
12.1. MEAN VALUE INTERPOLATION OF LAGRANGE TYPE 198
12.2. KERGIN INTERPOLATION AND THE SCALE OF MEAN VALUE INTERPOLATIONS
203 NOTES AND REFERENCES 205
CHAPTER 13. MULTIVARIATE POLYNOMIAL INTERPOLATIONS ARISING BY
HYPERPLANES 206 13.1. POINTWISE INTERPOLATION 206
13.2. POLYNOMIAL INTERPOLATION BY TRACES ON MANIFOLDS 209
13.3. SPECIAL CASES AND CONSEQUENCES 224
13.3.1. INTERPOLATION ON THE SPHERE BY HOMOGENEOUS POLYNOMIALS 224
13.3.2. HERMITE INTERPOLATION 226
13.3.3. TENSOR-PRODUCT INTERPOLATION 226
13.3.4. FINITE DEMENT INTERPOLATIONS 227
NOTES AND REFERENCES 230
CHAPTER 14. MULTIVARIATE POINTWISE INTERPOLATION 231
14.1. BIRKHOFF INTERPOLATION 231
14.2. SHIFTS OF SETS AND DIFFERENTIATION OF THE VANDERMONDE DETERMINANT
D-^Z) 236
14.3. QUADRATIC TRANSFORMATIONS 245
14.4. HERMITE INTERPOLATION 247
14.5. THE BIRKHOFF DIAGONAL INTERPOLATION 258
14.6. UNIFORM HERMITE INTERPOLATION 260
NOTES AND REFERENCES 263
REFERENCES 265
INDEX 273
NOTATION 275
|
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| spelling | Bojanov, Borislav D. Verfasser (DE-588)121035212 aut Spline functions and multivariate interpolations by B. D. Bojanov, H. A. Hakopian and A. A. Sahakian Dordrecht [u.a.] Kluwer 1993 IX, 276 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 248 Literaturverz. S. 265 - 272 Splines, théorie des ram Interpolation Spline theory Spline-Interpolation (DE-588)4182396-5 gnd rswk-swf Spline-Funktion (DE-588)4056332-7 gnd rswk-swf Mehrdimensionale Interpolation (DE-588)4221362-9 gnd rswk-swf Spline-Funktion (DE-588)4056332-7 s Mehrdimensionale Interpolation (DE-588)4221362-9 s DE-604 Spline-Interpolation (DE-588)4182396-5 s Hakopian, Hakop A. Verfasser aut Sahakian, Artur A. Verfasser aut Mathematics and its applications 248 (DE-604)BV008163334 248 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005024537&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bojanov, Borislav D. Hakopian, Hakop A. Sahakian, Artur A. Spline functions and multivariate interpolations Mathematics and its applications Splines, théorie des ram Interpolation Spline theory Spline-Interpolation (DE-588)4182396-5 gnd Spline-Funktion (DE-588)4056332-7 gnd Mehrdimensionale Interpolation (DE-588)4221362-9 gnd |
| subject_GND | (DE-588)4182396-5 (DE-588)4056332-7 (DE-588)4221362-9 |
| title | Spline functions and multivariate interpolations |
| title_auth | Spline functions and multivariate interpolations |
| title_exact_search | Spline functions and multivariate interpolations |
| title_full | Spline functions and multivariate interpolations by B. D. Bojanov, H. A. Hakopian and A. A. Sahakian |
| title_fullStr | Spline functions and multivariate interpolations by B. D. Bojanov, H. A. Hakopian and A. A. Sahakian |
| title_full_unstemmed | Spline functions and multivariate interpolations by B. D. Bojanov, H. A. Hakopian and A. A. Sahakian |
| title_short | Spline functions and multivariate interpolations |
| title_sort | spline functions and multivariate interpolations |
| topic | Splines, théorie des ram Interpolation Spline theory Spline-Interpolation (DE-588)4182396-5 gnd Spline-Funktion (DE-588)4056332-7 gnd Mehrdimensionale Interpolation (DE-588)4221362-9 gnd |
| topic_facet | Splines, théorie des Interpolation Spline theory Spline-Interpolation Spline-Funktion Mehrdimensionale Interpolation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005024537&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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