## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Wednesday, May 14, 2014, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Hemant Tyagi

## Interpolation with cubic splines

Consider an unknown function f: [a,b] -> R and say we are given values f(x_0),...f(x_n) on a mesh: x_0 (= a) < x_1 < ... < x_n ( = b). The interpolation problem involves finding an interpolant Q of f on the mesh such that Q(x_i) = f(x_i) for all points on the mesh. The aim is to find an interpolant that approximates the unknown f well, in the sense that as the maximum distance between any two points on the mesh goes to 0, then the approximation error between Q and f (in the infinity norm) also goes to zero. We will review this problem and analyze a popular class of interpolants namely cubic splines which are piece-wise cubic polynomials and are also smooth.

Information for students and suggested topics for student talks

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