CsSmooth Class

Extension of the Spline class to construct a smooth cubic spline from noisy data points.

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

System.Object
Imsl.Math.Spline
Imsl.Math.CsSmooth

public class CsSmooth : 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 CsSmooth 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 = xData, but it does not interpolate the data . The smoothing spline S is the unique function that minimizes

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

subject to the constraint

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

where $\sigma$ is the smoothing parameter. The reader should consult Reinsch (1967) for more information concerning smoothing splines. CsSmooth solves the above problem when the user provides the smoothing parameter $\sigma$ . CsSmoothC2 attempts to find the "optimal" smoothing parameter using the statistical technique known as cross-validation. This means that (in a very rough sense) one chooses the value of $\sigma$ so that the smoothing spline $(S_\sigma)$ best approximates the value of the data at , if it is computed using all the data except the i-th; this is true for all $i = 0, \ldots, n-1$ . For more information on this topic, we refer the reader to Craven and Wahba (1979).

Requirements

Namespace: Imsl.Math

Assembly: ImslCS (in ImslCS.dll)

CsSmooth Class

Thread Safety

Remarks

Requirements

See Also