Approximation of set-valued functions :: adaptation of classical approximation operators /
This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Hackensack, NJ :
Imperial College Press,
[2014]
|
| Subjects: | |
| Online Access: | DE-862 DE-863 |
| Summary: | This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D cross-sections. This is reflected in the focus of this book, which is the approximation of set-valued functions with general (not necessarily convex) sets as values, while previo. |
| Physical Description: | 1 online resource (xiii, 153 pages) |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9781783263035 1783263032 |
Staff View
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn894894787 | ||
| 003 | OCoLC | ||
| 005 | 20250103110447.0 | ||
| 006 | m o d | ||
| 007 | cr mn||||||||| | ||
| 008 | 141110t20142014nju ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e rda |e pn |c N$T |d YDXCP |d N$T |d OCLCQ |d N$T |d OCLCQ |d CDX |d OCLCQ |d CUS |d OCLCQ |d E7B |d OSU |d DEBSZ |d EBLCP |d COO |d OCLCQ |d AGLDB |d OCLCQ |d VTS |d CEF |d TKN |d STF |d M8D |d UKAHL |d OCLCQ |d OCLCO |d OCLCQ |d OCLCO |d OCLCL |d SXB |d OCLCQ |d OCLCO | ||
| 019 | |a 895432259 |a 974443237 |a 974565200 | ||
| 020 | |a 9781783263035 |q (electronic bk.) | ||
| 020 | |a 1783263032 |q (electronic bk.) | ||
| 020 | |z 9781783263028 |q (hardcover ; |q alk. paper) | ||
| 020 | |z 1783263024 |q (hardcover ; |q alk. paper) | ||
| 035 | |a (OCoLC)894894787 |z (OCoLC)895432259 |z (OCoLC)974443237 |z (OCoLC)974565200 | ||
| 050 | 4 | |a QA221 |b .D94 2014eb | |
| 072 | 7 | |a MAT |x 005000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 034000 |2 bisacsh | |
| 082 | 7 | |a 515/.8 |2 23 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Dyn, N. |q (Nira), |e author. |1 https://id.oclc.org/worldcat/entity/E39PBJppFCXWfP3bMrXdGtPRKd |0 http://id.loc.gov/authorities/names/no97066815 | |
| 245 | 1 | 0 | |a Approximation of set-valued functions : |b adaptation of classical approximation operators / |c Nira Dyn, Tel Aviv University, Israel, Elza Farkhi, Tel Aviv University, Israel, Alona Mokhov, Tel Aviv University, Israel. |
| 264 | 1 | |a Hackensack, NJ : |b Imperial College Press, |c [2014] | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource (xiii, 153 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 520 | |a This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D cross-sections. This is reflected in the focus of this book, which is the approximation of set-valued functions with general (not necessarily convex) sets as values, while previo. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Preface; Contents; Notations; I Scientific Background; 1. On Functions with Values in Metric Spaces; 1.1 Basic Notions; 1.2 Basic Approximation Methods; 1.3 Classical Approximation Operators; 1.3.1 Positive operators; 1.3.2 Interpolation operators; 1.3.3 Spline subdivision schemes; 1.4 Bibliographical Notes; 2. On Sets; 2.1 Sets and Operations Between Sets; 2.1.1 Definitions and notation; 2.1.2 Minkowski linear combination; 2.1.3 Metric average; 2.1.4 Metric linear combination; 2.2 Parametrizations of Sets; 2.2.1 Induced metrics and operations; 2.2.2 Convex sets by support functions. | |
| 505 | 8 | |a 2.2.3 Parametrization of sets in R2.2.4 Star-shaped sets by radial functions; 2.2.5 General sets by signed distance functions; 2.3 Bibliographical Notes; 3. On Set-Valued Functions (SVFs); 3.1 Definitions and Examples; 3.2 Representations of SVFs; 3.3 Regularity Based on Representations; 3.4 Bibliographical Notes; II Approximation of SVFs with Images in Rn; 4. Methods Based on Canonical Representations; 4.1 Induced Operators; 4.2 Approximation Results; 4.3 Application to SVFs with Convex Images; 4.4 Examples and Conclusions; 4.5 Bibliographical Notes. | |
| 505 | 8 | |a 5. Methods Based on Minkowski Convex Combinations5.1 Spline Subdivision Schemes for Convex Sets; 5.2 Non-Convexity Measures of a Compact Set; 5.3 Convexification of Sequences of Sample-Based Positive Operators; 5.4 Convexification by Spline Subdivision Schemes; 5.5 Bibliographical Notes; 6. Methods Based on the Metric Average; 6.1 Schoenberg Spline Operators; 6.2 Spline Subdivision Schemes; 6.3 Bernstein Polynomial Operators; 6.4 Bibliographical Notes; 7. Methods Based on Metric Linear Combinations; 7.1 Metric Piecewise Linear Interpolation; 7.2 Error Analysis. | |
| 505 | 8 | |a 7.3 Multifunctions with Convex Images7.4 Specific Metric Operators; 7.4.1 Metric Bernstein operators; 7.4.2 Metric Schoenberg operators; 7.4.3 Metric polynomial interpolation; 7.5 Bibliographical Notes; 8. Methods Based on Metric Selections; 8.1 Metric Selections; 8.2 Approximation Results; 8.3 Bibliographical Notes; III Approximation of SVFs with Images in R; 9. SVFs with Images in R; 9.1 Preliminaries on the Graphs of SVFs; 9.2 Continuity of the Boundaries of a CBV Multifunction; 9.3 Regularity Properties of the Boundaries; 10. Multi-Segmental and Topological Representations. | |
| 505 | 8 | |a 10.1 Multi-Segmental Representations (MSRs)10.2 Topological MSRs; 10.2.1 Existence of a topological MSR; 10.2.2 Conditions for uniqueness of a TMSR; 10.3 Representation by Topological Selections; 10.4 Regularity of SVFs Based on MSRs; 11. Methods Based on Topological Representation; 11.1 Positive Linear Operators Based on TMSRs; 11.1.1 Bernstein polynomial operators; 11.1.2 Schoenberg operators; 11.2 General Operators Based on Topological Selections; 11.3 Bibliographical Notes to Part III; Bibliography; Index. | |
| 650 | 0 | |a Approximation theory. |0 http://id.loc.gov/authorities/subjects/sh85006190 | |
| 650 | 0 | |a Linear operators. |0 http://id.loc.gov/authorities/subjects/sh85077178 | |
| 650 | 0 | |a Function spaces. |0 http://id.loc.gov/authorities/subjects/sh85052310 | |
| 650 | 6 | |a Théorie de l'approximation. | |
| 650 | 6 | |a Opérateurs linéaires. | |
| 650 | 6 | |a Espaces fonctionnels. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Approximation theory |2 fast | |
| 650 | 7 | |a Function spaces |2 fast | |
| 650 | 7 | |a Linear operators |2 fast | |
| 700 | 1 | |a Farkhi, Elza, |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjtgXCGqkGqfBGqhKX7d33 |0 http://id.loc.gov/authorities/names/n2014035208 | |
| 700 | 1 | |a Mokhov, Alona, |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjFQGx8FK3Hy3kcc8QqVcq |0 http://id.loc.gov/authorities/names/n2014035210 | |
| 758 | |i has work: |a Approximation of set-valued functions (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGwmB6Vr7bVK7T3Mwxy6Dm |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Dyn, N. (Nira). |t Approximation of set-valued functions |z 9781783263028 |w (DLC) 2014023451 |w (OCoLC)849719556 |
| 966 | 4 | 0 | |l DE-862 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=886753 |3 Volltext |
| 966 | 4 | 0 | |l DE-863 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=886753 |3 Volltext |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH27217353 | ||
| 938 | |a Coutts Information Services |b COUT |n 30119982 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL1835769 | ||
| 938 | |a ebrary |b EBRY |n ebr10983895 | ||
| 938 | |a EBSCOhost |b EBSC |n 886753 | ||
| 938 | |a YBP Library Services |b YANK |n 12148760 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-862 | ||
| 049 | |a DE-863 | ||
Record in the Search Index
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn894894787 |
|---|---|
| _version_ | 1829095016682749952 |
| adam_text | |
| any_adam_object | |
| author | Dyn, N. (Nira) Farkhi, Elza Mokhov, Alona |
| author_GND | http://id.loc.gov/authorities/names/no97066815 http://id.loc.gov/authorities/names/n2014035208 http://id.loc.gov/authorities/names/n2014035210 |
| author_facet | Dyn, N. (Nira) Farkhi, Elza Mokhov, Alona |
| author_role | aut aut aut |
| author_sort | Dyn, N. |
| author_variant | n d nd e f ef a m am |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA221 |
| callnumber-raw | QA221 .D94 2014eb |
| callnumber-search | QA221 .D94 2014eb |
| callnumber-sort | QA 3221 D94 42014EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Preface; Contents; Notations; I Scientific Background; 1. On Functions with Values in Metric Spaces; 1.1 Basic Notions; 1.2 Basic Approximation Methods; 1.3 Classical Approximation Operators; 1.3.1 Positive operators; 1.3.2 Interpolation operators; 1.3.3 Spline subdivision schemes; 1.4 Bibliographical Notes; 2. On Sets; 2.1 Sets and Operations Between Sets; 2.1.1 Definitions and notation; 2.1.2 Minkowski linear combination; 2.1.3 Metric average; 2.1.4 Metric linear combination; 2.2 Parametrizations of Sets; 2.2.1 Induced metrics and operations; 2.2.2 Convex sets by support functions. 2.2.3 Parametrization of sets in R2.2.4 Star-shaped sets by radial functions; 2.2.5 General sets by signed distance functions; 2.3 Bibliographical Notes; 3. On Set-Valued Functions (SVFs); 3.1 Definitions and Examples; 3.2 Representations of SVFs; 3.3 Regularity Based on Representations; 3.4 Bibliographical Notes; II Approximation of SVFs with Images in Rn; 4. Methods Based on Canonical Representations; 4.1 Induced Operators; 4.2 Approximation Results; 4.3 Application to SVFs with Convex Images; 4.4 Examples and Conclusions; 4.5 Bibliographical Notes. 5. Methods Based on Minkowski Convex Combinations5.1 Spline Subdivision Schemes for Convex Sets; 5.2 Non-Convexity Measures of a Compact Set; 5.3 Convexification of Sequences of Sample-Based Positive Operators; 5.4 Convexification by Spline Subdivision Schemes; 5.5 Bibliographical Notes; 6. Methods Based on the Metric Average; 6.1 Schoenberg Spline Operators; 6.2 Spline Subdivision Schemes; 6.3 Bernstein Polynomial Operators; 6.4 Bibliographical Notes; 7. Methods Based on Metric Linear Combinations; 7.1 Metric Piecewise Linear Interpolation; 7.2 Error Analysis. 7.3 Multifunctions with Convex Images7.4 Specific Metric Operators; 7.4.1 Metric Bernstein operators; 7.4.2 Metric Schoenberg operators; 7.4.3 Metric polynomial interpolation; 7.5 Bibliographical Notes; 8. Methods Based on Metric Selections; 8.1 Metric Selections; 8.2 Approximation Results; 8.3 Bibliographical Notes; III Approximation of SVFs with Images in R; 9. SVFs with Images in R; 9.1 Preliminaries on the Graphs of SVFs; 9.2 Continuity of the Boundaries of a CBV Multifunction; 9.3 Regularity Properties of the Boundaries; 10. Multi-Segmental and Topological Representations. 10.1 Multi-Segmental Representations (MSRs)10.2 Topological MSRs; 10.2.1 Existence of a topological MSR; 10.2.2 Conditions for uniqueness of a TMSR; 10.3 Representation by Topological Selections; 10.4 Regularity of SVFs Based on MSRs; 11. Methods Based on Topological Representation; 11.1 Positive Linear Operators Based on TMSRs; 11.1.1 Bernstein polynomial operators; 11.1.2 Schoenberg operators; 11.2 General Operators Based on Topological Selections; 11.3 Bibliographical Notes to Part III; Bibliography; Index. |
| ctrlnum | (OCoLC)894894787 |
| dewey-full | 515/.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.8 |
| dewey-search | 515/.8 |
| dewey-sort | 3515 18 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06887cam a2200709 i 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn894894787</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20250103110447.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr mn|||||||||</controlfield><controlfield tag="008">141110t20142014nju ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">N$T</subfield><subfield code="b">eng</subfield><subfield code="e">rda</subfield><subfield code="e">pn</subfield><subfield code="c">N$T</subfield><subfield code="d">YDXCP</subfield><subfield code="d">N$T</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">N$T</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">CDX</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">CUS</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">E7B</subfield><subfield code="d">OSU</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">EBLCP</subfield><subfield code="d">COO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AGLDB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">CEF</subfield><subfield code="d">TKN</subfield><subfield code="d">STF</subfield><subfield code="d">M8D</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield><subfield code="d">SXB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">895432259</subfield><subfield code="a">974443237</subfield><subfield code="a">974565200</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781783263035</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1783263032</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9781783263028</subfield><subfield code="q">(hardcover ;</subfield><subfield code="q">alk. paper)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">1783263024</subfield><subfield code="q">(hardcover ;</subfield><subfield code="q">alk. paper)</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)894894787</subfield><subfield code="z">(OCoLC)895432259</subfield><subfield code="z">(OCoLC)974443237</subfield><subfield code="z">(OCoLC)974565200</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA221</subfield><subfield code="b">.D94 2014eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">005000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">034000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">515/.8</subfield><subfield code="2">23</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dyn, N.</subfield><subfield code="q">(Nira),</subfield><subfield code="e">author.</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PBJppFCXWfP3bMrXdGtPRKd</subfield><subfield code="0">http://id.loc.gov/authorities/names/no97066815</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Approximation of set-valued functions :</subfield><subfield code="b">adaptation of classical approximation operators /</subfield><subfield code="c">Nira Dyn, Tel Aviv University, Israel, Elza Farkhi, Tel Aviv University, Israel, Alona Mokhov, Tel Aviv University, Israel.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Hackensack, NJ :</subfield><subfield code="b">Imperial College Press,</subfield><subfield code="c">[2014]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2014</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xiii, 153 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D cross-sections. This is reflected in the focus of this book, which is the approximation of set-valued functions with general (not necessarily convex) sets as values, while previo.</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Preface; Contents; Notations; I Scientific Background; 1. On Functions with Values in Metric Spaces; 1.1 Basic Notions; 1.2 Basic Approximation Methods; 1.3 Classical Approximation Operators; 1.3.1 Positive operators; 1.3.2 Interpolation operators; 1.3.3 Spline subdivision schemes; 1.4 Bibliographical Notes; 2. On Sets; 2.1 Sets and Operations Between Sets; 2.1.1 Definitions and notation; 2.1.2 Minkowski linear combination; 2.1.3 Metric average; 2.1.4 Metric linear combination; 2.2 Parametrizations of Sets; 2.2.1 Induced metrics and operations; 2.2.2 Convex sets by support functions.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2.2.3 Parametrization of sets in R2.2.4 Star-shaped sets by radial functions; 2.2.5 General sets by signed distance functions; 2.3 Bibliographical Notes; 3. On Set-Valued Functions (SVFs); 3.1 Definitions and Examples; 3.2 Representations of SVFs; 3.3 Regularity Based on Representations; 3.4 Bibliographical Notes; II Approximation of SVFs with Images in Rn; 4. Methods Based on Canonical Representations; 4.1 Induced Operators; 4.2 Approximation Results; 4.3 Application to SVFs with Convex Images; 4.4 Examples and Conclusions; 4.5 Bibliographical Notes.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">5. Methods Based on Minkowski Convex Combinations5.1 Spline Subdivision Schemes for Convex Sets; 5.2 Non-Convexity Measures of a Compact Set; 5.3 Convexification of Sequences of Sample-Based Positive Operators; 5.4 Convexification by Spline Subdivision Schemes; 5.5 Bibliographical Notes; 6. Methods Based on the Metric Average; 6.1 Schoenberg Spline Operators; 6.2 Spline Subdivision Schemes; 6.3 Bernstein Polynomial Operators; 6.4 Bibliographical Notes; 7. Methods Based on Metric Linear Combinations; 7.1 Metric Piecewise Linear Interpolation; 7.2 Error Analysis.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">7.3 Multifunctions with Convex Images7.4 Specific Metric Operators; 7.4.1 Metric Bernstein operators; 7.4.2 Metric Schoenberg operators; 7.4.3 Metric polynomial interpolation; 7.5 Bibliographical Notes; 8. Methods Based on Metric Selections; 8.1 Metric Selections; 8.2 Approximation Results; 8.3 Bibliographical Notes; III Approximation of SVFs with Images in R; 9. SVFs with Images in R; 9.1 Preliminaries on the Graphs of SVFs; 9.2 Continuity of the Boundaries of a CBV Multifunction; 9.3 Regularity Properties of the Boundaries; 10. Multi-Segmental and Topological Representations.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">10.1 Multi-Segmental Representations (MSRs)10.2 Topological MSRs; 10.2.1 Existence of a topological MSR; 10.2.2 Conditions for uniqueness of a TMSR; 10.3 Representation by Topological Selections; 10.4 Regularity of SVFs Based on MSRs; 11. Methods Based on Topological Representation; 11.1 Positive Linear Operators Based on TMSRs; 11.1.1 Bernstein polynomial operators; 11.1.2 Schoenberg operators; 11.2 General Operators Based on Topological Selections; 11.3 Bibliographical Notes to Part III; Bibliography; Index.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Approximation theory.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85006190</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Linear operators.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85077178</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Function spaces.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85052310</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Théorie de l'approximation.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Opérateurs linéaires.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Espaces fonctionnels.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Calculus.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Mathematical Analysis.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Approximation theory</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Function spaces</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Linear operators</subfield><subfield code="2">fast</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Farkhi, Elza,</subfield><subfield code="e">author.</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjtgXCGqkGqfBGqhKX7d33</subfield><subfield code="0">http://id.loc.gov/authorities/names/n2014035208</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Mokhov, Alona,</subfield><subfield code="e">author.</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjFQGx8FK3Hy3kcc8QqVcq</subfield><subfield code="0">http://id.loc.gov/authorities/names/n2014035210</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Approximation of set-valued functions (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCGwmB6Vr7bVK7T3Mwxy6Dm</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Dyn, N. (Nira).</subfield><subfield code="t">Approximation of set-valued functions</subfield><subfield code="z">9781783263028</subfield><subfield code="w">(DLC) 2014023451</subfield><subfield code="w">(OCoLC)849719556</subfield></datafield><datafield tag="966" ind1="4" ind2="0"><subfield code="l">DE-862</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=886753</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="4" ind2="0"><subfield code="l">DE-863</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=886753</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH27217353</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Coutts Information Services</subfield><subfield code="b">COUT</subfield><subfield code="n">30119982</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest Ebook Central</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL1835769</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10983895</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">886753</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">12148760</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-862</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn894894787 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-11T08:42:19Z |
| institution | BVB |
| isbn | 9781783263035 1783263032 |
| language | English |
| oclc_num | 894894787 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xiii, 153 pages) |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Imperial College Press, |
| record_format | marc |
| spelling | Dyn, N. (Nira), author. https://id.oclc.org/worldcat/entity/E39PBJppFCXWfP3bMrXdGtPRKd http://id.loc.gov/authorities/names/no97066815 Approximation of set-valued functions : adaptation of classical approximation operators / Nira Dyn, Tel Aviv University, Israel, Elza Farkhi, Tel Aviv University, Israel, Alona Mokhov, Tel Aviv University, Israel. Hackensack, NJ : Imperial College Press, [2014] ©2014 1 online resource (xiii, 153 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D cross-sections. This is reflected in the focus of this book, which is the approximation of set-valued functions with general (not necessarily convex) sets as values, while previo. Includes bibliographical references and index. Print version record. Preface; Contents; Notations; I Scientific Background; 1. On Functions with Values in Metric Spaces; 1.1 Basic Notions; 1.2 Basic Approximation Methods; 1.3 Classical Approximation Operators; 1.3.1 Positive operators; 1.3.2 Interpolation operators; 1.3.3 Spline subdivision schemes; 1.4 Bibliographical Notes; 2. On Sets; 2.1 Sets and Operations Between Sets; 2.1.1 Definitions and notation; 2.1.2 Minkowski linear combination; 2.1.3 Metric average; 2.1.4 Metric linear combination; 2.2 Parametrizations of Sets; 2.2.1 Induced metrics and operations; 2.2.2 Convex sets by support functions. 2.2.3 Parametrization of sets in R2.2.4 Star-shaped sets by radial functions; 2.2.5 General sets by signed distance functions; 2.3 Bibliographical Notes; 3. On Set-Valued Functions (SVFs); 3.1 Definitions and Examples; 3.2 Representations of SVFs; 3.3 Regularity Based on Representations; 3.4 Bibliographical Notes; II Approximation of SVFs with Images in Rn; 4. Methods Based on Canonical Representations; 4.1 Induced Operators; 4.2 Approximation Results; 4.3 Application to SVFs with Convex Images; 4.4 Examples and Conclusions; 4.5 Bibliographical Notes. 5. Methods Based on Minkowski Convex Combinations5.1 Spline Subdivision Schemes for Convex Sets; 5.2 Non-Convexity Measures of a Compact Set; 5.3 Convexification of Sequences of Sample-Based Positive Operators; 5.4 Convexification by Spline Subdivision Schemes; 5.5 Bibliographical Notes; 6. Methods Based on the Metric Average; 6.1 Schoenberg Spline Operators; 6.2 Spline Subdivision Schemes; 6.3 Bernstein Polynomial Operators; 6.4 Bibliographical Notes; 7. Methods Based on Metric Linear Combinations; 7.1 Metric Piecewise Linear Interpolation; 7.2 Error Analysis. 7.3 Multifunctions with Convex Images7.4 Specific Metric Operators; 7.4.1 Metric Bernstein operators; 7.4.2 Metric Schoenberg operators; 7.4.3 Metric polynomial interpolation; 7.5 Bibliographical Notes; 8. Methods Based on Metric Selections; 8.1 Metric Selections; 8.2 Approximation Results; 8.3 Bibliographical Notes; III Approximation of SVFs with Images in R; 9. SVFs with Images in R; 9.1 Preliminaries on the Graphs of SVFs; 9.2 Continuity of the Boundaries of a CBV Multifunction; 9.3 Regularity Properties of the Boundaries; 10. Multi-Segmental and Topological Representations. 10.1 Multi-Segmental Representations (MSRs)10.2 Topological MSRs; 10.2.1 Existence of a topological MSR; 10.2.2 Conditions for uniqueness of a TMSR; 10.3 Representation by Topological Selections; 10.4 Regularity of SVFs Based on MSRs; 11. Methods Based on Topological Representation; 11.1 Positive Linear Operators Based on TMSRs; 11.1.1 Bernstein polynomial operators; 11.1.2 Schoenberg operators; 11.2 General Operators Based on Topological Selections; 11.3 Bibliographical Notes to Part III; Bibliography; Index. Approximation theory. http://id.loc.gov/authorities/subjects/sh85006190 Linear operators. http://id.loc.gov/authorities/subjects/sh85077178 Function spaces. http://id.loc.gov/authorities/subjects/sh85052310 Théorie de l'approximation. Opérateurs linéaires. Espaces fonctionnels. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Approximation theory fast Function spaces fast Linear operators fast Farkhi, Elza, author. https://id.oclc.org/worldcat/entity/E39PCjtgXCGqkGqfBGqhKX7d33 http://id.loc.gov/authorities/names/n2014035208 Mokhov, Alona, author. https://id.oclc.org/worldcat/entity/E39PCjFQGx8FK3Hy3kcc8QqVcq http://id.loc.gov/authorities/names/n2014035210 has work: Approximation of set-valued functions (Text) https://id.oclc.org/worldcat/entity/E39PCGwmB6Vr7bVK7T3Mwxy6Dm https://id.oclc.org/worldcat/ontology/hasWork Print version: Dyn, N. (Nira). Approximation of set-valued functions 9781783263028 (DLC) 2014023451 (OCoLC)849719556 |
| spellingShingle | Dyn, N. (Nira) Farkhi, Elza Mokhov, Alona Approximation of set-valued functions : adaptation of classical approximation operators / Preface; Contents; Notations; I Scientific Background; 1. On Functions with Values in Metric Spaces; 1.1 Basic Notions; 1.2 Basic Approximation Methods; 1.3 Classical Approximation Operators; 1.3.1 Positive operators; 1.3.2 Interpolation operators; 1.3.3 Spline subdivision schemes; 1.4 Bibliographical Notes; 2. On Sets; 2.1 Sets and Operations Between Sets; 2.1.1 Definitions and notation; 2.1.2 Minkowski linear combination; 2.1.3 Metric average; 2.1.4 Metric linear combination; 2.2 Parametrizations of Sets; 2.2.1 Induced metrics and operations; 2.2.2 Convex sets by support functions. 2.2.3 Parametrization of sets in R2.2.4 Star-shaped sets by radial functions; 2.2.5 General sets by signed distance functions; 2.3 Bibliographical Notes; 3. On Set-Valued Functions (SVFs); 3.1 Definitions and Examples; 3.2 Representations of SVFs; 3.3 Regularity Based on Representations; 3.4 Bibliographical Notes; II Approximation of SVFs with Images in Rn; 4. Methods Based on Canonical Representations; 4.1 Induced Operators; 4.2 Approximation Results; 4.3 Application to SVFs with Convex Images; 4.4 Examples and Conclusions; 4.5 Bibliographical Notes. 5. Methods Based on Minkowski Convex Combinations5.1 Spline Subdivision Schemes for Convex Sets; 5.2 Non-Convexity Measures of a Compact Set; 5.3 Convexification of Sequences of Sample-Based Positive Operators; 5.4 Convexification by Spline Subdivision Schemes; 5.5 Bibliographical Notes; 6. Methods Based on the Metric Average; 6.1 Schoenberg Spline Operators; 6.2 Spline Subdivision Schemes; 6.3 Bernstein Polynomial Operators; 6.4 Bibliographical Notes; 7. Methods Based on Metric Linear Combinations; 7.1 Metric Piecewise Linear Interpolation; 7.2 Error Analysis. 7.3 Multifunctions with Convex Images7.4 Specific Metric Operators; 7.4.1 Metric Bernstein operators; 7.4.2 Metric Schoenberg operators; 7.4.3 Metric polynomial interpolation; 7.5 Bibliographical Notes; 8. Methods Based on Metric Selections; 8.1 Metric Selections; 8.2 Approximation Results; 8.3 Bibliographical Notes; III Approximation of SVFs with Images in R; 9. SVFs with Images in R; 9.1 Preliminaries on the Graphs of SVFs; 9.2 Continuity of the Boundaries of a CBV Multifunction; 9.3 Regularity Properties of the Boundaries; 10. Multi-Segmental and Topological Representations. 10.1 Multi-Segmental Representations (MSRs)10.2 Topological MSRs; 10.2.1 Existence of a topological MSR; 10.2.2 Conditions for uniqueness of a TMSR; 10.3 Representation by Topological Selections; 10.4 Regularity of SVFs Based on MSRs; 11. Methods Based on Topological Representation; 11.1 Positive Linear Operators Based on TMSRs; 11.1.1 Bernstein polynomial operators; 11.1.2 Schoenberg operators; 11.2 General Operators Based on Topological Selections; 11.3 Bibliographical Notes to Part III; Bibliography; Index. Approximation theory. http://id.loc.gov/authorities/subjects/sh85006190 Linear operators. http://id.loc.gov/authorities/subjects/sh85077178 Function spaces. http://id.loc.gov/authorities/subjects/sh85052310 Théorie de l'approximation. Opérateurs linéaires. Espaces fonctionnels. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Approximation theory fast Function spaces fast Linear operators fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85006190 http://id.loc.gov/authorities/subjects/sh85077178 http://id.loc.gov/authorities/subjects/sh85052310 |
| title | Approximation of set-valued functions : adaptation of classical approximation operators / |
| title_auth | Approximation of set-valued functions : adaptation of classical approximation operators / |
| title_exact_search | Approximation of set-valued functions : adaptation of classical approximation operators / |
| title_full | Approximation of set-valued functions : adaptation of classical approximation operators / Nira Dyn, Tel Aviv University, Israel, Elza Farkhi, Tel Aviv University, Israel, Alona Mokhov, Tel Aviv University, Israel. |
| title_fullStr | Approximation of set-valued functions : adaptation of classical approximation operators / Nira Dyn, Tel Aviv University, Israel, Elza Farkhi, Tel Aviv University, Israel, Alona Mokhov, Tel Aviv University, Israel. |
| title_full_unstemmed | Approximation of set-valued functions : adaptation of classical approximation operators / Nira Dyn, Tel Aviv University, Israel, Elza Farkhi, Tel Aviv University, Israel, Alona Mokhov, Tel Aviv University, Israel. |
| title_short | Approximation of set-valued functions : |
| title_sort | approximation of set valued functions adaptation of classical approximation operators |
| title_sub | adaptation of classical approximation operators / |
| topic | Approximation theory. http://id.loc.gov/authorities/subjects/sh85006190 Linear operators. http://id.loc.gov/authorities/subjects/sh85077178 Function spaces. http://id.loc.gov/authorities/subjects/sh85052310 Théorie de l'approximation. Opérateurs linéaires. Espaces fonctionnels. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Approximation theory fast Function spaces fast Linear operators fast |
| topic_facet | Approximation theory. Linear operators. Function spaces. Théorie de l'approximation. Opérateurs linéaires. Espaces fonctionnels. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Approximation theory Function spaces Linear operators |
| work_keys_str_mv | AT dynn approximationofsetvaluedfunctionsadaptationofclassicalapproximationoperators AT farkhielza approximationofsetvaluedfunctionsadaptationofclassicalapproximationoperators AT mokhovalona approximationofsetvaluedfunctionsadaptationofclassicalapproximationoperators |