CsSmoothC2 Class

Extension of the Spline class used to construct a spline for noisy data points using an alternate method.

For a list of all members of this type, see CsSmoothC2 Members.

System.Object
Imsl.Math.Spline
Imsl.Math.CsSmoothC2

public class CsSmoothC2 : 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 CsSmoothC2 is designed to produce a cubic spline approximation to a data set in which the function values are noisy. This spline is called a smoothing spline. It is a natural cubic spline with knots at all the data abscissas x, but it does not interpolate the data . The smoothing spline $S_\sigma$ is the unique function that minimizes

$\int\limits_a^b {s''_\sigma \left( x \right)^2 dx}$

subject to the constraint

$\sum\limits_{i=0}^{n-1} {\left| {s_\sigma \left( {x_i } \right) - f_i } \right|} ^2 \le \sigma$

Recommended values for $\sigma$ depend on the weights, w. If an estimate for the standard deviation of the error in the y-values is availiable, then should be set to this value and the smoothing parameter should be choosen in the confidence interval corresponding to the left side of the above inequality. That is,

$n-\sqrt{2n} \le \sigma \le n+\sqrt{2n}$

CsSmoothC2 is based on an algorithm of Reinsch (1967). This algorithm is also discussed in de Boor (1978, pages 235-243).

Requirements

Namespace: Imsl.Math

Assembly: ImslCS (in ImslCS.dll)

CsSmoothC2 Class

Thread Safety

Remarks

Requirements

See Also