Shape-preserving approximation by real and complex polynomials:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2008
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 329 - 349 |
| Beschreibung: | XIII, 352 S. 25 cm |
| ISBN: | 9780817647025 0817647023 9780817647032 |
Internformat
MARC
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| 100 | 1 | |a Gal, Sorin G. |d 1953- |e Verfasser |0 (DE-588)121815943 |4 aut | |
| 245 | 1 | 0 | |a Shape-preserving approximation by real and complex polynomials |c Sorin G. Gal. [Consulting ed.: George A. Anastassiou] |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2008 | |
| 300 | |a XIII, 352 S. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 329 - 349 | ||
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| 856 | 4 | 2 | |u http://d-nb.info/983973741/04 |3 Inhaltsverzeichnis |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017054006 | ||
Datensatz im Suchindex
| _version_ | 1804138526124539904 |
|---|---|
| adam_text | Contents
Preface
Vil
1
Shape-Preserving Approximation by Real Univariate
Polynomials
............................................... 1
1.1
Introduction
............................................ 1
1.2
Shape-Preserving Interpolation by Polynomials
.............. 7
1.3 Bernstein
-Туре
Polynomials Preserving Shapes
.............. 19
1.4
Shisha-Type Results
..................................... 35
1.5
Positive and Copositive Polynomial Approximation
.......... 38
1.5.1
Pointwise Positive Approximation
................... 38
1.5.2 LP-Positive
Approximation,
0 <
ρ
<
oo
............... 39
1.5.3
Uniform and Pointwise Copositive Approximation
..... 41
1.5.4
£P-Copositive Approximation,
0 <
ρ
<
oo
............ 47
1.5.5
Copositive Approximation with Modified Weighted
Moduli of Smoothness
............................. 48
1.5.6
Generalizations
................................... 50
1.6
Monotone and Comonotone Polynomial Approximation
...... 54
1.6.1
¿^-Monotone Approximation,
0 <
ρ
<
oo
............. 57
1.6.2
Pointwise Monotone Approximation
................. 62
1.6.3
I^-Comonotone Approximation,
0 <
ρ
<
oo
........... 64
1.6.4
Comonotone Approximation with Modified Weighted
Moduli of Smoothness
............................. 68
1.6.5
Nearly Comonotone Approximation
.................. 70
1.7
Convex and Coconvex Polynomial Approximation
........... 73
1.7.1
Linear Methods in Convex Approximation
............ 74
1.7.2
Nonlinear Methods in Convex Approximation
......... 80
1.7.3
Pointwise Convex Approximation
.................... 81
1.7.4
Convex Approximation with Modified Weighted
Moduli of Smoothness
............................. 82
1.7.5
Uniform Coconvex Approximation
................... 83
Contents
1.7.6 Coconvex Approximation
with Modified Weighted
Moduli of Smoothness
............................. 85
1.7.7
Pointwise Coconvex Approximation
.................. 86
1.7.8
Nearly Coconvex Approximation
.................... 87
1.8
Shape-Preserving Approximation by Convolution Polynomials
. 90
1.9
Positive Linear Polynomial Operators Preserving Shape
...... 94
1.10
Notes
.................................................. 95
Shape-Preserving Approximation by Real Multivariate
Polynomials
............................................... 99
2.1
Introduction
............................................ 99
2.2
Bernstein-Type Polynomials Preserving Shapes
..............114
2.3
Shisha-Type Methods and Generalizations
..................126
2.3.1
Shisha-Type Approximation
........................126
2.3.2
Х
-Positive
Approximation
..........................129
2.4
Approximation Preserving Three Classical Shapes
...........133
2.4.1
Harmonic Polynomial Approximation
................133
2.4.2
Subharmonic Polynomial Approximation
.............136
2.4.3
Convex Polynomial Approximation
..................138
2.5
Bivariate Monotone Approximation by Convolution
Polynomials
............................................154
2.6
Tensor Product Polynomials Preserving Popoviciu s
Convexities
.............................................160
2.6.1
Bivariate/Multivariate Monotone and Convex
Approximation
....................................160
2.6.2
Concepts in Bivariate Coshape Approximation
........178
2.6.3
Bivariate Copositive Approximation
.................186
2.6.4
Bivariate Comonotone Approximation
...............194
2.6.5
Bivariate Shape-Preserving Interpolation
.............207
2.7
Bibliographical Notes and Open Problems
..................209
Shape-Preserving Approximation by Complex Univariate
Polynomials
...............................................215
3.1
Introduction
............................................215
3.2
Shisha-Type Methods and Generalizations
..................224
3.2.1
Shisha-Type Approximation
........................230
3.2.2
Re[L]-Positive Approximation
.......................235
3.3
Shape-Preserving Approximation by Convolution
Polynomials
............................................239
3.3.1
Bell-Shaped Kernels and Complex Convolutions
.......240
3.3.2
Geometric and Approximation Properties of Various
Complex Convolutions
.............................247
3.4
Approximation and Geometric Properties of Bernstein
Polynomials
............................................263
3.5
Bibliographical Notes and Open Problems
..................280
Contents xiii
4
Shape-Preserving
Approximation
by Complex
Multivariate Polynomials
..................................283
4.1
Introduction
............................................283
4.2 Bernstein
-Туре
Polynomials Preserving Univalence
..........286
4.3
Shape-Preserving Approximation by Other Types
of Polynomials
..........................................290
4.4
Bibliographical Notes and Open Problems
..................302
5
Appendix: Some Related Topics
...........................305
5.1
Shape-Preserving Approximation by General Linear
Operators on C[a, b]
.....................................305
5.2
Some Real and Complex Nonpolynomial Operators
Preserving Shape
........................................309
5.3
Shape-Preserving Polynomial Approximation
in Ordered Vector Spaces
.................................312
5.4
Complex Nonpolynomial Convolutions Preserving Shape
.....316
5.5
Bibliographical Notes and Open Problems
..................323
References
.....................................................329
Index
..........................................................351
|
| any_adam_object | 1 |
| author | Gal, Sorin G. 1953- |
| author_GND | (DE-588)121815943 |
| author_facet | Gal, Sorin G. 1953- |
| author_role | aut |
| author_sort | Gal, Sorin G. 1953- |
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| building | Verbundindex |
| bvnumber | BV035248323 |
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| classification_tum | MAT 412f MAT 300f MAT 320f |
| ctrlnum | (OCoLC)440766975 (DE-599)DNB983973741 |
| dewey-full | 511.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.42 |
| dewey-search | 511.42 |
| dewey-sort | 3511.42 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035248323 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:29:35Z |
| institution | BVB |
| isbn | 9780817647025 0817647023 9780817647032 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017054006 |
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| physical | XIII, 352 S. 25 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Gal, Sorin G. 1953- Verfasser (DE-588)121815943 aut Shape-preserving approximation by real and complex polynomials Sorin G. Gal. [Consulting ed.: George A. Anastassiou] Boston [u.a.] Birkhäuser 2008 XIII, 352 S. 25 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 329 - 349 Polynomapproximation (DE-588)4197097-4 gnd rswk-swf Polynomapproximation (DE-588)4197097-4 s DE-604 http://d-nb.info/983973741/04 Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017054006&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gal, Sorin G. 1953- Shape-preserving approximation by real and complex polynomials Polynomapproximation (DE-588)4197097-4 gnd |
| subject_GND | (DE-588)4197097-4 |
| title | Shape-preserving approximation by real and complex polynomials |
| title_auth | Shape-preserving approximation by real and complex polynomials |
| title_exact_search | Shape-preserving approximation by real and complex polynomials |
| title_full | Shape-preserving approximation by real and complex polynomials Sorin G. Gal. [Consulting ed.: George A. Anastassiou] |
| title_fullStr | Shape-preserving approximation by real and complex polynomials Sorin G. Gal. [Consulting ed.: George A. Anastassiou] |
| title_full_unstemmed | Shape-preserving approximation by real and complex polynomials Sorin G. Gal. [Consulting ed.: George A. Anastassiou] |
| title_short | Shape-preserving approximation by real and complex polynomials |
| title_sort | shape preserving approximation by real and complex polynomials |
| topic | Polynomapproximation (DE-588)4197097-4 gnd |
| topic_facet | Polynomapproximation |
| url | http://d-nb.info/983973741/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017054006&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT galsoring shapepreservingapproximationbyrealandcomplexpolynomials |
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