Convergence of Comonotone Histopolating Splines

Abstract

The convergence rate of histopolation on an interval with combined splines of class C¹ having linear/linear rational or quadratic polynomial pieces is studied. The function to histopolate may have finite number of derivative zeros and established convergence rate depends mainly on the behaviour of the derivative near its zeros. Given numerical results are completely consistent with theoretical ones.

Keywords:

• histopolation
• rational spline
• quadratic spline
• convergence rate
• comonotone shape-preserving

AMS Subject Classification:

• 65D07
• 41A15
• 41A25