🚀 go-pugleaf

In article <1992Dec24.110843.29860@cv.ruu.nl> ger@cv.ruu.nl (Ger Timmens) writes:
#I want the singular value decomposition of a 3x3 matrix.
#I currently use the algorithm of numerical recipes.
#However I think a much simpler algorithm should be out there.
#
#Any pointers ?

You've run into a situation that frustrates a lot of people.  In
principle, it should be possible to solve eigenvalue (or singular
value) problems of order 2, 3, and 4 directly using the formulas for
solving quadratic, cubic, and quartic equations.  In practice, though,
the complexity of the formulas makes the effort practical only for 2x2
problems.  And even then the difficulties are great.  When Charlie Van
Loan (of Golub and Van Loan fame) was a graduate student he produced a
forty page manuscript entitled "An Algorithm for the Generalized
Matrix Eigenvalue Problem {$Ax=\lambda Bx$} for the Important Case
{$N=2$}", and it was none too short.  You will probably do well to
stick with general code.

Not that I recommend the Numerical Recipes code.  I've been told that
it is a modification of the LINPACK code, the modifications causing
it to fail in some cases.  I would stick with the LINPACK or LAPACK
code which is available on netlib.

Pete Stewart