Approximation by spline functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1989
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 223 - 239 |
| Physical Description: | XI, 243 S. |
| ISBN: | 3540516182 0387516182 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV002468713 | ||
| 003 | DE-604 | ||
| 005 | 20031023 | ||
| 007 | t | ||
| 008 | 891127s1989 gw |||| 00||| eng d | ||
| 020 | |a 3540516182 |9 3-540-51618-2 | ||
| 020 | |a 0387516182 |9 0-387-51618-2 | ||
| 035 | |a (OCoLC)246731172 | ||
| 035 | |a (DE-599)BVBBV002468713 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-12 |a DE-91 |a DE-91G |a DE-703 |a DE-739 |a DE-355 |a DE-824 |a DE-29T |a DE-N2 |a DE-20 |a DE-19 |a DE-706 |a DE-634 |a DE-188 |a DE-11 | ||
| 084 | |a SK 470 |0 (DE-625)143241: |2 rvk | ||
| 084 | |a MAT 413f |2 stub | ||
| 100 | 1 | |a Nürnberger, Günther |d 1948- |e Verfasser |0 (DE-588)1012100243 |4 aut | |
| 245 | 1 | 0 | |a Approximation by spline functions |c Günther Nürnberger |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1989 | |
| 300 | |a XI, 243 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 223 - 239 | ||
| 650 | 0 | 7 | |a Spline-Approximation |0 (DE-588)4182394-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Approximationstheorie |0 (DE-588)4120913-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Beste Approximation |0 (DE-588)4144932-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Čebyšev-Approximation |0 (DE-588)4147433-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Interpolation |0 (DE-588)4162121-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Spline-Funktion |0 (DE-588)4056332-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Beste Approximation |0 (DE-588)4144932-0 |D s |
| 689 | 0 | 1 | |a Spline-Funktion |0 (DE-588)4056332-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Interpolation |0 (DE-588)4162121-9 |D s |
| 689 | 1 | 1 | |a Spline-Funktion |0 (DE-588)4056332-7 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Spline-Funktion |0 (DE-588)4056332-7 |D s |
| 689 | 2 | 1 | |a Approximationstheorie |0 (DE-588)4120913-8 |D s |
| 689 | 2 | |5 DE-604 | |
| 689 | 3 | 0 | |a Spline-Approximation |0 (DE-588)4182394-1 |D s |
| 689 | 3 | |5 DE-604 | |
| 689 | 4 | 0 | |a Čebyšev-Approximation |0 (DE-588)4147433-8 |D s |
| 689 | 4 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001594739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001594739 | ||
Record in the Search Index
| _version_ | 1804116881459642368 |
|---|---|
| adam_text | Contents
Chapter I. Polynomials and Chebyshev Spaces
1. Interpolation by Chebyshev Spaces 1
1.1. Lagrange Interpolation by Chebyshev Spaces 1
1.2. Hermite Interpolation by Extended Chebyshev Spaces 4
1.3. Characterization of Extended Complete Chebyshev Spaces 7
1.4. Further Properties of Chebyshev Spaces 11
1.5. Variation Diminishing Property of Order Complete
Chebyshev Spaces 15
2. Interpolation by Polynomials and Divided Differences 16
2.1. Divided Differences 17
2.2. Newton Form of Interpolating Polynomials 21
2.3. Nearly Optimal Interpolation Points 25
3. Best Uniform Approximation by Chebyshev Spaces 29
3.1. Best Approximation in Normed Linear Spaces 29
3.2. Characterization of Best Uniform Approximations 32
3.3. Global Unicity and Strong Unicity of Best Uniform
Approximations 36
3.4. Algorithm 48
3.5. Approximation Power of Polynomials 54
4. Best Li Approximation by Chebyshev Spaces 56
4.1. Global Unicity of Best .^ Approximations 56
4.2. Interpolation at Canonical Points 60
5. Best One Sided Zi Approximation by Chebyshev Spaces and
Quadrature Formulas 65
5.1. Unicity of Best One Sided /^ Approximations 65
5.2. Gauss Quadrature Formulas for Chebyshev Spaces 69
6. Best Z2~Approximation 76
X Contents
Chapter II. Splines and Weak Chebyshev Spaces
1. Weak Chebyshev Spaces 80
1.1. Basic Properties 80
1.2. Best Uniform Approximation by Weak Chebyshev Spaces 88
1.3. Spline Spaces 93
2. B Splines 95
2.1. Basic Properties 95
2.2. B Spline Basis 98
2.3. Recurrence Relations 99
2.4. Variation Diminishing Property 106
3. Interpolation by Splines 107
3.1. Lagrange and Hermite Interpolation by Splines 107
3.2. Interpolation by Complete Splines, Periodic Splines
and Natural Splines 115
3.3. Quasi Interpolation 127
4. Best Uniform Approximation by Splines 131
4.1. Characterization, Unicity and Strong Unicity of Best
Uniform Approximations 132
4.2. Algorithm (Fixed Knots) 143
4.3. Algorithm (Free Knots) 150
4.4. Approximation Power of Splines 159
5. Continuity of the Set Valued Metric Projection for Spline Spaces ... 161
5.1. Upper Semicontinuity 162
5.2. Lower Semicontinuity 163
5.3. Continuous Selections 164
6. Best L —Approximation by Weak Chebyshev Spaces 168
6.1. Unicity of Best .^ Approximations 169
6.2. Interpolation at Canonical Points 171
7. Best One Sided Li Approximation by Weak Chebyshev
Spaces and Quadrature Formulas 174
7.1. Unicity of Best One Sided L Approximations 174
7.2. Gauss Quadrature Formulas for Weak Chebyshev Spaces 176
8. Approximation of Linear Functionals and Splines 180
9. Spaces of Splines with Multiple Knots 187
Contents XI
Appendix
1. Splines with Free Knots 190
2. Splines in Two Variables 195
2.1. Tensor Product and Blending 195
2.2. Finite Element Functions 200
2.3. Spline Functions 205
3. Spline Collocation and Differential Equations 218
References 223
Index 240
|
| any_adam_object | 1 |
| author | Nürnberger, Günther 1948- |
| author_GND | (DE-588)1012100243 |
| author_facet | Nürnberger, Günther 1948- |
| author_role | aut |
| author_sort | Nürnberger, Günther 1948- |
| author_variant | g n gn |
| building | Verbundindex |
| bvnumber | BV002468713 |
| classification_rvk | SK 470 |
| classification_tum | MAT 413f |
| ctrlnum | (OCoLC)246731172 (DE-599)BVBBV002468713 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02248nam a2200553 c 4500</leader><controlfield tag="001">BV002468713</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20031023 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">891127s1989 gw |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540516182</subfield><subfield code="9">3-540-51618-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387516182</subfield><subfield code="9">0-387-51618-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)246731172</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002468713</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-N2</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 470</subfield><subfield code="0">(DE-625)143241:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 413f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Nürnberger, Günther</subfield><subfield code="d">1948-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1012100243</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Approximation by spline functions</subfield><subfield code="c">Günther Nürnberger</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1989</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 243 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 223 - 239</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Spline-Approximation</subfield><subfield code="0">(DE-588)4182394-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Approximationstheorie</subfield><subfield code="0">(DE-588)4120913-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Beste Approximation</subfield><subfield code="0">(DE-588)4144932-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Čebyšev-Approximation</subfield><subfield code="0">(DE-588)4147433-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Interpolation</subfield><subfield code="0">(DE-588)4162121-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Spline-Funktion</subfield><subfield code="0">(DE-588)4056332-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Beste Approximation</subfield><subfield code="0">(DE-588)4144932-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Spline-Funktion</subfield><subfield code="0">(DE-588)4056332-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Interpolation</subfield><subfield code="0">(DE-588)4162121-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Spline-Funktion</subfield><subfield code="0">(DE-588)4056332-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Spline-Funktion</subfield><subfield code="0">(DE-588)4056332-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="1"><subfield code="a">Approximationstheorie</subfield><subfield code="0">(DE-588)4120913-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="3" ind2="0"><subfield code="a">Spline-Approximation</subfield><subfield code="0">(DE-588)4182394-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="4" ind2="0"><subfield code="a">Čebyšev-Approximation</subfield><subfield code="0">(DE-588)4147433-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="4" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001594739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001594739</subfield></datafield></record></collection> |
| id | DE-604.BV002468713 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:45:33Z |
| institution | BVB |
| isbn | 3540516182 0387516182 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001594739 |
| oclc_num | 246731172 |
| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-N2 DE-20 DE-19 DE-BY-UBM DE-706 DE-634 DE-188 DE-11 |
| owner_facet | DE-12 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-N2 DE-20 DE-19 DE-BY-UBM DE-706 DE-634 DE-188 DE-11 |
| physical | XI, 243 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Springer |
| record_format | marc |
| spelling | Nürnberger, Günther 1948- Verfasser (DE-588)1012100243 aut Approximation by spline functions Günther Nürnberger Berlin [u.a.] Springer 1989 XI, 243 S. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 223 - 239 Spline-Approximation (DE-588)4182394-1 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Beste Approximation (DE-588)4144932-0 gnd rswk-swf Čebyšev-Approximation (DE-588)4147433-8 gnd rswk-swf Interpolation (DE-588)4162121-9 gnd rswk-swf Spline-Funktion (DE-588)4056332-7 gnd rswk-swf Beste Approximation (DE-588)4144932-0 s Spline-Funktion (DE-588)4056332-7 s DE-604 Interpolation (DE-588)4162121-9 s Approximationstheorie (DE-588)4120913-8 s Spline-Approximation (DE-588)4182394-1 s Čebyšev-Approximation (DE-588)4147433-8 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001594739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nürnberger, Günther 1948- Approximation by spline functions Spline-Approximation (DE-588)4182394-1 gnd Approximationstheorie (DE-588)4120913-8 gnd Beste Approximation (DE-588)4144932-0 gnd Čebyšev-Approximation (DE-588)4147433-8 gnd Interpolation (DE-588)4162121-9 gnd Spline-Funktion (DE-588)4056332-7 gnd |
| subject_GND | (DE-588)4182394-1 (DE-588)4120913-8 (DE-588)4144932-0 (DE-588)4147433-8 (DE-588)4162121-9 (DE-588)4056332-7 |
| title | Approximation by spline functions |
| title_auth | Approximation by spline functions |
| title_exact_search | Approximation by spline functions |
| title_full | Approximation by spline functions Günther Nürnberger |
| title_fullStr | Approximation by spline functions Günther Nürnberger |
| title_full_unstemmed | Approximation by spline functions Günther Nürnberger |
| title_short | Approximation by spline functions |
| title_sort | approximation by spline functions |
| topic | Spline-Approximation (DE-588)4182394-1 gnd Approximationstheorie (DE-588)4120913-8 gnd Beste Approximation (DE-588)4144932-0 gnd Čebyšev-Approximation (DE-588)4147433-8 gnd Interpolation (DE-588)4162121-9 gnd Spline-Funktion (DE-588)4056332-7 gnd |
| topic_facet | Spline-Approximation Approximationstheorie Beste Approximation Čebyšev-Approximation Interpolation Spline-Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001594739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nurnbergergunther approximationbysplinefunctions |