Box splines:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer New York
2010
|
| Edition: | 1. ed., softcover version of original hardcover edition 1993 |
| Series: | Applied Mathematical Sciences
98 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XVII, 200 S. 57 schw.-w. Ill. 235 mm x 155 mm |
| ISBN: | 9781441928344 1441928340 |
Staff View
MARC
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| 245 | 1 | 0 | |a Box splines |c Carl de Boor ; Klaus Höllig ; Sherman Riemenschneider |
| 250 | |a 1. ed., softcover version of original hardcover edition 1993 | ||
| 264 | 1 | |a New York, NY |b Springer New York |c 2010 | |
| 300 | |a XVII, 200 S. |b 57 schw.-w. Ill. |c 235 mm x 155 mm | ||
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Record in the Search Index
| _version_ | 1805146809569378304 |
|---|---|
| adam_text |
їх
Contents
Preface v
Notation
xiii
Chapter I
·
Box splines defined
The analytic definition
1
A geometric description
2
The inductive definition
4
A univariate example
4
A bivariate example
5
Conventions
7
Basic properties
9
Fourier transform
9
Symmetries
Ю
Local structure and truncated power
11
Differentiation
13
Proof of basic properties
15
Recurrence relations
17
Example: four ways to construct a box spline
18
The support of the box spline
23
Zonotopes
27
Notes
30
Contents
Chapter II
·
The linear algebra of box spline spaces
Convolutions
34
Partition of unity
35
The box spline shifts which do not vanish at a given point
37
Differentiation
38
Linear independence
38
Example: the three-direction mesh
41
Example: the ZP element
41
The dimension of D(E)
42
Tensor products
46
Three-direction mesh
46
The structure of
Δ(Ξ)
48
Example: four-direction mesh with multiplicities
52
The polynomials contained in
S
52
A basis for D(E)
53
Examples
55
D- and
σ
-invariance
57
Notes
58
Chapter III
■
Quasi-interpolants
&
approximation power
An upper bound
62
Quasi-interpolants
63
Convolutions on polynomial spaces
65
The semi-discrete convolution is a convolution on its range
66
Marsden
identity
67
Quasi-interpolant summary
68
Appell
sequence
68
Example: the ZP element
69
Choice of the quasi-interpolant functional
72
Minimality
73
Quasi-interpolants via Neumann series
74
Quasi-interpolants via Fourier transform
76
Example: the ZP element
77
Notes
78
Contents xi
Chapter IV
■ Cardinal
interpolation k difference equations
Correct and singular cardinal interpolation
79
Example: univariate and bivariate quadratic box splines
80
Symbol and fundamental solution
81
Example: three-direction mesh
84
Correctness and linear independence
87
Example: centered hat function
88
Singular cardinal interpolation
92
Example: the centered ZP element
95
Bivariate four-direction box splines with even multiplicities
95
The approximation order of cardinal interpolation
99
Notes
101
Chapter V
·
Approximation by cardinal splines
&
wavelets
Fundamental domains
105
Properties of
ΩΞ
108
Example: two-direction mesh 111
Example: three-direction mesh
114
Convergence of cardinal splines
117
Relation to cardinal series
120
Example: three-direction mesh
122
Wavelet decompositions
124
Wavelets in dimensions
< 3 132
Notes
135
Chapter VI
·
Discrete box splines
&
linear diophantine equations
Definition
137
Geometric description
138
Support
138
Convolution
139
Construction
139
Fourier transform
140
Differentiation
141
Annihilation
142
Linear independence
142
Linear diophantine equations
144
Linear independence (continued)
148
On extending to an element of
Δ(Ξ)
151
xii
Contents
Discrete truncated power
154
The local structure of the discrete box spline
155
Local linear independence
156
Notes
157
Chapter
VII
·
Subdivision algorithms
Masks
160
Geometric derivation of the refinement equation
161
Factorization of the mask
162
Example: two-direction mesh
164
Subdivision as discrete smoothing
164
Linear convergence of subdivision
165
Example: linear convergence is best possible
168
Quadratic convergence of subdivision
169
Example: the ZP element
172
Notes
173
References
175
Index
193 |
| any_adam_object | 1 |
| author | De Boor, Carl 1937- Höllig, Klaus Riemenschneider, Sherman |
| author_GND | (DE-588)109311507 |
| author_facet | De Boor, Carl 1937- Höllig, Klaus Riemenschneider, Sherman |
| author_role | aut aut aut |
| author_sort | De Boor, Carl 1937- |
| author_variant | b c d bc bcd k h kh s r sr |
| building | Verbundindex |
| bvnumber | BV040254840 |
| classification_rvk | SK 470 |
| ctrlnum | (OCoLC)802347324 (DE-599)DNB1008421103 |
| discipline | Mathematik |
| edition | 1. ed., softcover version of original hardcover edition 1993 |
| format | Book |
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| indexdate | 2024-07-21T00:35:47Z |
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| isbn | 9781441928344 1441928340 |
| language | English |
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| physical | XVII, 200 S. 57 schw.-w. Ill. 235 mm x 155 mm |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer New York |
| record_format | marc |
| series | Applied Mathematical Sciences |
| series2 | Applied Mathematical Sciences |
| spelling | De Boor, Carl 1937- Verfasser (DE-588)109311507 aut Box splines Carl de Boor ; Klaus Höllig ; Sherman Riemenschneider 1. ed., softcover version of original hardcover edition 1993 New York, NY Springer New York 2010 XVII, 200 S. 57 schw.-w. Ill. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Applied Mathematical Sciences 98 Box spline (DE-588)4331592-6 gnd rswk-swf Spline (DE-588)4182391-6 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Spline (DE-588)4182391-6 s Mehrere Variable (DE-588)4277015-4 s 1\p DE-604 Box spline (DE-588)4331592-6 s 2\p DE-604 Höllig, Klaus Verfasser aut Riemenschneider, Sherman Verfasser aut Applied Mathematical Sciences 98 (DE-604)BV000005274 98 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3598607&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025110734&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | De Boor, Carl 1937- Höllig, Klaus Riemenschneider, Sherman Box splines Applied Mathematical Sciences Box spline (DE-588)4331592-6 gnd Spline (DE-588)4182391-6 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| subject_GND | (DE-588)4331592-6 (DE-588)4182391-6 (DE-588)4277015-4 |
| title | Box splines |
| title_auth | Box splines |
| title_exact_search | Box splines |
| title_full | Box splines Carl de Boor ; Klaus Höllig ; Sherman Riemenschneider |
| title_fullStr | Box splines Carl de Boor ; Klaus Höllig ; Sherman Riemenschneider |
| title_full_unstemmed | Box splines Carl de Boor ; Klaus Höllig ; Sherman Riemenschneider |
| title_short | Box splines |
| title_sort | box splines |
| topic | Box spline (DE-588)4331592-6 gnd Spline (DE-588)4182391-6 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| topic_facet | Box spline Spline Mehrere Variable |
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