Class DoubleLeastSquares computes the minimum-norm solution to a linear
system Ax = y.
Namespace:
CenterSpace.NMath.CoreAssembly: NMath (in NMath.dll) Version: 5.1.0.0
Syntax
| C# |
|---|
[SerializableAttribute] public class DoubleLeastSquares : ICloneable |
| Visual Basic (Declaration) |
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<SerializableAttribute> _ Public Class DoubleLeastSquares _ Implements ICloneable |
| Visual C++ |
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[SerializableAttribute] public ref class DoubleLeastSquares : ICloneable |
Remarks
In a least squares problem, we assume a linear model for
a quantity y that depends on one or more independent variables
a1, a2,...,an; that is, y = x0 + x1*a1 + ... + xn*an.
x0 is called the intercept parameter.
The goal of a least squares problem is to solve for the best values of x0, x1,...,xn. Several observations of the independent values ai are recorded, along with the corresponding values of the dependent variable y. If m observations are performed, and for the ith observation we denote the values of the independent variables ai1, ai2,...ain and the corresponding dependent value of y as yi, then we form the linear system Ax = y, where A = (aij) and y = (yi). The least squares solution is the value of x that minimizes ||Ax - y||.
Note that if the model contains a non-zero intercept parameter, then the first column of A is all ones. Class DoubleLeastSquares uses a complete orthogonal factorization of A to compute the solution. Matrix A is rectangular and may be rank deficient.
The goal of a least squares problem is to solve for the best values of x0, x1,...,xn. Several observations of the independent values ai are recorded, along with the corresponding values of the dependent variable y. If m observations are performed, and for the ith observation we denote the values of the independent variables ai1, ai2,...ain and the corresponding dependent value of y as yi, then we form the linear system Ax = y, where A = (aij) and y = (yi). The least squares solution is the value of x that minimizes ||Ax - y||.
Note that if the model contains a non-zero intercept parameter, then the first column of A is all ones. Class DoubleLeastSquares uses a complete orthogonal factorization of A to compute the solution. Matrix A is rectangular and may be rank deficient.
