BsLeastSquares Class

Extension of the BSpline class to compute a least squares spline approximation to data points.

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

System.Object
Imsl.Math.BSpline
Imsl.Math.BsLeastSquares

public class BsLeastSquares : BSpline

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

Let's make the identifications

n = xData.length

x = xData

f = yData

m = nCoef

k = order

For convenience, we assume that the sequence x is increasing, although the class does not require this.

By default, k = 4, and the knot sequence we select equally distributes the knots through the distinct ${x_i}'s$ . In particular, the m + k knots will be generated in with k knots stacked at each of the extreme values. The interior knots will be equally spaced in the interval.

Once knots ${\bf t}$ and weights w are determined, then the spline least-squares fit to the data is computed by minimizing over the linear coefficients

$\sum_{i=0}^{n-1} {w_i\biggl[f_i-\sum_{j=1}^{m}{a_jB_j(x_i)}\biggr]^2}$

where the are a (B-spline) basis for the spline subspace.

This algorithm is based on the routine L2APPR by deBoor (1978, p. 255).

Requirements

Namespace: Imsl.Math

Assembly: ImslCS (in ImslCS.dll)

BsLeastSquares Class

Thread Safety

Remarks

Requirements

See Also