Multivariate Splines and Algebraic Geometry

  • Henry K. Schenck

    University of Illinois, Urbana, United States
  • Larry L. Schumaker

    Vanderbilt University, Nashville, USA
  • Tatyana Sorokina

    Towson University, USA

Abstract

Multivariate splines are effective tools in numerical analysis and approximation theory. Despite an extensive literature on the subject, there remain open questions in finding their dimension, constructing local bases, and determining their approximation power. Much of what is currently known was developed by numerical analysts, using classical methods, in particular the so-called Bernstein-B´ezier techniques. Due to their many interesting structural properties, splines have become of keen interest to researchers in commutative and homological algebra and algebraic geometry. Unfortunately, these communities have not collaborated much. The purpose of the half-size workshop is to intensify the interaction between the different groups by bringing them together. This could lead to essential breakthroughs on several of the above problems.

Cite this article

Henry K. Schenck, Larry L. Schumaker, Tatyana Sorokina, Multivariate Splines and Algebraic Geometry. Oberwolfach Rep. 12 (2015), no. 2, pp. 1139–1200

DOI 10.4171/OWR/2015/21