Nonlinear Nonnested Spline Approximation
2017 (English)In: Constructive approximation, ISSN 0176-4276, E-ISSN 1432-0940Article in journal (Refereed) Epub ahead of print
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
Spline approximation, Multivariate approximation, Nonlinear approximation, Besov spaces, Jackson estimate, Bernstein estimate
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kau:diva-47876DOI: 10.1007/s00365-016-9361-3OAI: oai:DiVA.org:kau-47876DiVA: diva2:1072876