LeastSquares

LeastSquares[m,b]

finds an x that solves the linear least-squares problem for the matrix equation m.x==b.

Details and Options

  • LeastSquares[m,b] gives a vector x that minimizes Norm[m.x-b].
  • The vector x is uniquely determined by the minimization only if Length[x]==MatrixRank[m].
  • The argument b can be a matrix, in which case the least-squares minimization is done independently for each column in b, which is the x that minimizes Norm[m.x-b,"Frobenius"].
  • LeastSquares works on both numerical and symbolic matrices, as well as SparseArray objects.
  • A Method option can also be given. Settings for arbitrary-precision numerical matrices include "Direct" and "IterativeRefinement", and for sparse arrays "Direct" and "Krylov". The default setting of Automatic switches between these methods, depending on the matrix given.

Examples

open allclose all

Basic Examples  (1)

Solve a simple least-squares problem:

In[1]:=
Click for copyable input
Out[1]=

Scope  (4)

Generalizations & Extensions  (1)

Options  (1)

Applications  (1)

Properties & Relations  (6)

See Also

LinearSolve  PseudoInverse  Fit  LinearModelFit  SingularValueDecomposition  QRDecomposition  CoefficientArrays  DesignMatrix  FindFit  NMinimize  FindMinimum

Tutorials

Introduced in 2007
(6.0)