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.


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Basic Examples  (1)

Solve a simple least-squares problem:

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Scope  (4)

Generalizations & Extensions  (1)

Options  (1)

Applications  (1)

Properties & Relations  (6)

Introduced in 2007