Anisotropic spline approximation with non-uniform B-splines

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.

Keywords:

• Non-uniform splines
• approximation
• quasi-interpolation
• multivariate
• domain

AMS Subject Classifications:

• 41A15
• 41A25
• 41A63

Acknowledgements

The author would like to thank Ulrich Reif for helpful discussion and comments.

Notes

No potential conflict of interest was reported by the author.