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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.

There's a method using orthogonalization by plane rotations from
the book by J. C. Nash, "Compact Numerical Methods for Computers:
Linear Algebra and Function Minimisation," Wiley 1979.  If you use
it to orthogonalize the columns, you only get a basis for the
column space, not its orthogonal complement, though you get the
complete row-space and null-space.  I am pretty sure it
is not as efficient as the standard SVD algorithm in Linpack,
but it is very simple to program.

I used Nash's technique in an application involving an N-by-3 coefficient
matrix for linear predictive coding.  By some simple preprocessing
to remove the constant LPC coefficient, the matrix was transformed to
N-by-2.  With just two columns, only one plane rotation is needed to
get the SVD, and you can even explicitly compute the singular values
without performing the whole SVD.  But I think that in general,
an N-by-3 matrix has no such simple solution.

I've implemented Nash's algorithm in Fortran, Pascal, and C, and
can mail you code if you want it.

...Rick			perry@vu-vlsi.ee.vill.edu

Dr. Rick Perry, Department of Electrical and Computer Engineering
Villanova University, Villanova, PA 19085, 215-645-4969, hm: 215-259-8734