
Solve the general matrix equation A x = b for x.
The matrix A can be any general m × n matrix, b is a mdimensional and x a ndimensional vector. The Matrix contains A as its first n columns and b as its last column. The ndimensional solution is returned as a Matrix with n columns.
When the number of equations (m) is greater than the number of unknowns (n) the algorithm gives the best leastsquares solution. If on the contrary you have fewer equations than unknowns the solution will not be unique.
Singular value decomposition with backsubstitution. Zero will be substituted for eigenvalues smaller than tolerance · maximum_eigenvalue (when the usersupplied tolerance equals 0.0 a value of 2.2 · 10^{16} · number_of_unknowns will be used as tolerance).
See for more details: Golub & van Loan (1996) chapters 2 and 3.
© djmw, October 6, 1996