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Student[LinearAlgebra]

  

LeastSquares

  

compute a least squares solution to a set of equations

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

LeastSquares(A, B, options)

Parameters

A

-

Matrix or set

B

-

column Vector or set of variables

options

-

(optional) parameters; for a complete list, see LinearAlgebra[LeastSquares]

Description

• 

For Matrix A and Vector B, the LeastSquares(A, B) command returns a Vector that best satisfies the condition A.x is approximately equal to B, in the least squares sense. The result that is returned is the Vector x which minimizes Norm(A . x - B, 2).

• 

Parameter A can also be a set of equations that describe the linear least squares problem. In this case, B is the set of variables in which the equations in A occur.

Examples

withStudent[LinearAlgebra]:

A3,0,4|2,3,4:

b1,2,4:

XLeastSquaresA,b

X:=35162562125

(1)

NormA.Xb

1625

(2)

Emx+ny3=0,2xy+2=0:

Vx,y:

LeastSquaresE,V

x=2n3m+2n,y=2m+3m+2n

(3)

See Also

LinearAlgebra[LeastSquares]

Student[LinearAlgebra]

Student[LinearAlgebra][LinearSolve]

Student[LinearAlgebra][Norm]

 


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