[Work] SVD

There exists a very powerful set of techniques for dealing with sets of equations
or matrices that are either singular or else numerically very close to singular. In many
cases where Gaussian elimination and LU decomposition fail to give satisfactory
results, this set of techniques, known as singular value decomposition, or SVD,
will diagnose for you precisely what the problem is. In some cases, SVD will
not only diagnose the problem, it will also solve it, in the sense of giving you a
useful numerical answer, although, as we shall see, not necessarily “the” answer
that you thought you should get.

SVD is also the method of choice for solving most linear least-squares problems.
We will outline the relevant theory in this section, but defer detailed discussion of
the use of SVD in this application to Chapter 15, whose subject is the parametric
modeling of data.

-- from Numerical Recipes