Spline represents and evaluates univariate piecewise polynomial splines.

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
[SerializableAttribute]
public abstract class Spline
Visual Basic (Declaration)
<SerializableAttribute> _
Public MustInherit Class Spline
Visual C++
[SerializableAttribute]
public ref class Spline abstract

Remarks

A univariate piecewise polynomial (function) p(x) is specified by giving its breakpoint sequence breakPoint[]= \xi \in {\bf R}^n, the order k (degree k-1) of its polynomial pieces,and the k \times (n-1) matrix coef=c of its local polynomial coefficients. In terms of this information, the piecewise polynomial (ppoly) function is given by

p(x) = \sum_{j=1}^k c_{ji} \frac{(x-\xi_i)^{j-1}}{(j-1)!} \;\;{\rm for}\; \xi_i \le x \le \xi_{i+1}
The breakpoint sequence \xi is assumed to be strictly increasing, and we extend the ppoly function to the entire real axis by extrapolation from the first and last intervals.

Inheritance Hierarchy

See Also