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

Details and OptionsDetails 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.
Introduced in 2007