NMath Reference Guide

## Double |

Class DoubleCOWeightedLeastSq solves weighted least squares problems
by using a Complete Orthogonal (CO) decomposition technique.

Inheritance Hierarchy

Syntax

The DoubleCOWeightedLeastSq type exposes the following members.

Constructors

Name | Description | |
---|---|---|

DoubleCOWeightedLeastSq | Default constructor. Instances created with this constructor will be empty and unsuable until the Factor method is called. | |

DoubleCOWeightedLeastSq(DoubleMatrix, DoubleVector) | Constructs a DoubleCOWeightedLeastSq instance from the given matrix and weights. | |

DoubleCOWeightedLeastSq(DoubleMatrix, DoubleVector, Boolean) | Constructs a DoubleCOWeightedLeastSq instance from the given matrix and weights. |

Properties

Methods

Name | Description | |
---|---|---|

Clone | Creates a deep copy of this weighted least squares instance. | |

Factor(DoubleMatrix, DoubleVector) | Performs any factorization on the matrix A necessary before computing a solution to the weighted least squares problem. | |

Factor(DoubleMatrix, DoubleVector, Boolean) | Performs any factorization on the matrix A necessary before computing a solution to the weighted least squares problem. | |

ResidualNormSqr | Computes the 2-norm squared of the residual vector. | |

ResidualVector | Computes and returns the residual vector. | |

Reweight | Performs necessary computations for a change of weights. | |

Solve | Compute the solution to the weighted least squares problem. |

Remarks

Use class DoubleCOWeightedLeastSq to find the minimal weighted
norm solution to the overdetermined linear system:
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

C#

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

See Also