Class DoubleCOWeightedLeastSq solves weighted least squares problems
by using a Complete Orthogonal (CO) decomposition technique.
Namespace:
CenterSpace.NMath.MatrixAssembly: NMath (in NMath.dll) Version: 5.1.0.0
Syntax
| C# |
|---|
[SerializableAttribute] public class DoubleCOWeightedLeastSq |
| Visual Basic (Declaration) |
|---|
<SerializableAttribute> _ Public Class DoubleCOWeightedLeastSq |
| Visual C++ |
|---|
[SerializableAttribute] public ref class DoubleCOWeightedLeastSq |
Remarks
Use class DoubleCOWeightedLeastSq to find the minimal weighted
norm solution to the overdetermined linear system:
CopyC#
That is, find the vector x that minimizes the 2-norm of the
weighted residual vector (D^-1/2)*(Ax - b). Where D is a digaonal matrix
with non-negative values on the diagonal. Prerequisites on the matrix
A are that it has more rows than columns, and is of full
rank.
The Alogorithm satisfies an accuracy bound that is not affected by ill
conditioning in the weight matrix D.
Reference: Complete Orthogonal Decomposition For Weighted Least Squares Patricia D. Hough and Stephen A. Vavasis SIAM J. Matrix Anal. Appl. Vol. 18, No. 2, pp 369-392, April 1997
CopyC#Ax = b
Reference: Complete Orthogonal Decomposition For Weighted Least Squares Patricia D. Hough and Stephen A. Vavasis SIAM J. Matrix Anal. Appl. Vol. 18, No. 2, pp 369-392, April 1997
