Anisotropic spline approximation with non-uniform B-splines. Issue 2 (25th January 2018)

• Record Type: Journal Article
• Authors: Sissouno, N.
• Is Part Of: Applicable analysis. Volume 97:Issue 2(2018)
• Page Start: 135
• Page End: 144
• Publication Date: 2018-01-25
• Subjects: Non-uniform splines -- approximation -- quasi-interpolation -- multivariate -- domain; 41A15 -- 41A25 -- 41A63; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1254774
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : Recently the author and U. Reif introduced the concept of diversification of uniform tensor product B-splines. Based on this concept, we give a new constructive modification of non-uniform B-splines. The resulting spline spaces are perfectly fitted for the approximation of functions defined on domains . We build a bounded quasi-interpolant and prove that for our spline spaces an anisotropic error estimate in the -norm, , is valid. In particular, we show that the constant of the error estimate does not depend on the shape of or the knot grid.