Matrix: Solve equation...

Solve the general matrix equation A x = b for x.

The matrix A can be any general m × n matrix, b is a m-dimensional and x a n-dimensional vector. The Matrix contains A as its first n columns and b as its last column. The n-dimensional 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 least-squares solution. If on the contrary you have fewer equations than unknowns the solution will not be unique.

Method

Singular value decomposition with backsubstitution. Zero will be substituted for eigenvalues smaller than tolerance · maximum_eigenvalue (when the user-supplied 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