Chebyshev blossoming in Müntz spaces: Toward shaping with Young diagrams

Handle URI:
http://hdl.handle.net/10754/562877
Title:
Chebyshev blossoming in Müntz spaces: Toward shaping with Young diagrams
Authors:
Ait-Haddou, Rachid; Sakane, Yusuke; Nomura, Taishin
Abstract:
The notion of a blossom in extended Chebyshev spaces offers adequate generalizations and extra-utilities to the tools for free-form design schemes. Unfortunately, such advantages are often overshadowed by the complexity of the resulting algorithms. In this work, we show that for the case of Müntz spaces with integer exponents, the notion of a Chebyshev blossom leads to elegant algorithms whose complexities are embedded in the combinatorics of Schur functions. We express the blossom and the pseudo-affinity property in Müntz spaces in terms of Schur functions. We derive an explicit expression for the Chebyshev-Bernstein basis via an inductive argument on nested Müntz spaces. We also reveal a simple algorithm for dimension elevation. Free-form design schemes in Müntz spaces with Young diagrams as shape parameters are discussed. © 2013 Elsevier Ltd. All rights reserved.
KAUST Department:
Visual Computing Center (VCC)
Publisher:
Elsevier BV
Journal:
Journal of Computational and Applied Mathematics
Issue Date:
Aug-2013
DOI:
10.1016/j.cam.2013.01.009
ARXIV:
arXiv:1107.2392
Type:
Article
ISSN:
03770427
Sponsors:
This work was partially supported by the MEXT Global COE project.
Additional Links:
http://arxiv.org/abs/arXiv:1107.2392v1
Appears in Collections:
Articles; Visual Computing Center (VCC)

Full metadata record

DC FieldValue Language
dc.contributor.authorAit-Haddou, Rachiden
dc.contributor.authorSakane, Yusukeen
dc.contributor.authorNomura, Taishinen
dc.date.accessioned2015-08-03T11:13:47Zen
dc.date.available2015-08-03T11:13:47Zen
dc.date.issued2013-08en
dc.identifier.issn03770427en
dc.identifier.doi10.1016/j.cam.2013.01.009en
dc.identifier.urihttp://hdl.handle.net/10754/562877en
dc.description.abstractThe notion of a blossom in extended Chebyshev spaces offers adequate generalizations and extra-utilities to the tools for free-form design schemes. Unfortunately, such advantages are often overshadowed by the complexity of the resulting algorithms. In this work, we show that for the case of Müntz spaces with integer exponents, the notion of a Chebyshev blossom leads to elegant algorithms whose complexities are embedded in the combinatorics of Schur functions. We express the blossom and the pseudo-affinity property in Müntz spaces in terms of Schur functions. We derive an explicit expression for the Chebyshev-Bernstein basis via an inductive argument on nested Müntz spaces. We also reveal a simple algorithm for dimension elevation. Free-form design schemes in Müntz spaces with Young diagrams as shape parameters are discussed. © 2013 Elsevier Ltd. All rights reserved.en
dc.description.sponsorshipThis work was partially supported by the MEXT Global COE project.en
dc.publisherElsevier BVen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1107.2392v1en
dc.subjectChebyshev blossomingen
dc.subjectChebyshev-Bernstein basisen
dc.subjectComputer aided designen
dc.subjectExtended Chebyshev systemsen
dc.subjectSchur functionsen
dc.subjectYoung diagramsen
dc.titleChebyshev blossoming in Müntz spaces: Toward shaping with Young diagramsen
dc.typeArticleen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalJournal of Computational and Applied Mathematicsen
dc.contributor.institutionDepartment of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, 560-0043 Osaka, Japanen
dc.contributor.institutionCenter of Advanced Medical Engineering and Informatics, Osaka University, 560-8531 Osaka, Japanen
dc.contributor.institutionDepartment of Mechanical Science and Bioengineering, Graduate School of Engineering Science, Osaka University, 560-8531 Osaka, Japanen
dc.identifier.arxividarXiv:1107.2392en
kaust.authorAit-Haddou, Rachiden
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