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Nonlinear Nonnested Spline Approximation
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.ORCID iD: 0000-0002-1752-1211
University of South Carolina.
2017 (English)In: Constructive approximation, ISSN 0176-4276, E-ISSN 1432-0940Article in journal (Refereed) Epub ahead of print
Abstract [en]

Nonlinear approximation from regular piecewise polynomials (splines) supported on rings in R2 is studied. By definition, a ring is a set in R2 obtained by subtracting a compact convex set with polygonal boundary from another such a set, but without creating uncontrollably narrow elongated subregions. Nested structure of the rings is not assumed; however, uniform boundedness of the eccentricities of the underlying convex sets is required. It is also assumed that the splines have maximum smoothness. Bernstein type inequalities for this sort of splines are proved that allow us to establish sharp inverse estimates in terms of Besov spaces.

Place, publisher, year, edition, pages
Springer, 2017.
Keyword [en]
Spline approximation, Multivariate approximation, Nonlinear approximation, Besov spaces, Jackson estimate, Bernstein estimate
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-47876DOI: 10.1007/s00365-016-9361-3OAI: oai:DiVA.org:kau-47876DiVA: diva2:1072876
Available from: 2017-02-09 Created: 2017-02-09 Last updated: 2017-02-13Bibliographically approved

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