CsPeriodic Class

Extension of the Spline class to interpolate data points with periodic boundary conditions.

For a list of all members of this type, see CsPeriodic Members.

System.Object
Imsl.Math.Spline
Imsl.Math.CsPeriodic

public class CsPeriodic : Spline

Thread Safety

Public static (Shared in Visual Basic) members of this type are safe for multithreaded operations. Instance members are not guaranteed to be thread-safe.

Remarks

Class CsPeriodic computes a cubic spline interpolant to a set of data points for $i =0,\ldots n-1$ . The breakpoints of the spline are the abscissas. The program enforces periodic endpoint conditions. This means that the spline s satisfies s(a) = s(b), ${\it{s'}}\left( {\it{a}} \right) = {\it{s'}}\left( {\it{b}} \right)$ , and $s''\left( a \right) = s''\left( b \right)$ , where a is the leftmost abscissa and b is the rightmost abscissa. If the ordinate values corresponding to a and b are not equal, then a warning message is issued. The ordinate value at b is set equal to the ordinate value at a and the interpolant is computed.

If the data points arise from the values of a smooth (say ) periodic function f, i.e. , then the error will behave in a predictable fashion. Let $\xi$ be the breakpoint vector for the above spline interpolant. Then, the maximum absolute error satisfies

$|f-s|_{[\xi_0,\xi_{n-1}]} \le C |f^{(4)}|_{[{\xi_0 ,\xi_{n-1} }]} |\xi|^4$

where

$|\xi|\;: = \max_{i=1,\ldots,n-1} |\xi_i - \xi_{i - 1} |$

For more details, see de Boor (1978, pages 320-322).

Requirements

Namespace: Imsl.Math

Assembly: ImslCS (in ImslCS.dll)

CsPeriodic Class

Thread Safety

Remarks

Requirements

See Also