Chapter 3

Polynomial Splines

Krystyna STYš and Tadeusz STYš

Abstract

In the chapter, the space S<sub>m</sub>(Δ,m − 1) of piecewise polynomial splines of degree m and differentiable up to the order m − 1 is introduced. In particular, the space S<sub>1</sub>(Δ, 0) of piecewise linear splines and the space S<sub>3</sub>(Δ, 2) of cubic splines are determined . Theorems on interpolation by the splines are stated and proved. The space S<sub>11</sub>(Δ, 0, 0) of belinear splines and the space S<sub>33</sub>(Δ, 2, 2) of be-cubic splines in two variables defined on rectangular grids are presented. On triangular grids the spaces Π<sub>1</sub> (Δ) and Π<sub>3</sub> (Δ) are considered. Mathematica modules have been designed for solving problems associated with application of splines. The chapter ends with a set of questions.

Total Pages: 63-102 (40)

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