Chebyshev blossoming in Müntz spaces: Toward shaping with Young diagrams

Rachid Ait-Haddou, Yusuke Sakane, Taishin Nomura

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)172-208
Number of pages37
JournalJournal of Computational and Applied Mathematics
Volume247
Issue number1
DOIs
StatePublished - Aug 2013

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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