Barton,
I am confident that things like the 2-norm and singular values are in
the lapack package. There are two difficulties here.
1. There is no documentation yet (that I know of concerning the lapack
package), and
more seriously, (and selfishly for me)
2. There are many situations which need higher
than standard double precision calculations with matrices.
One way of dealing with this is to use a combination of rational
arithmetic, symbolic calculations, conversion to bfloat, and
standard numerical techniques.
Since you already have eigen_by_jacobi, it only takes a line each to add
svd, 2-norm, and the 2-norm condition number.
svd(A):= reverse(sort(sqrt(eigens_by_jacobi(transpose(A).A))[1]))$
mat_norm_2(A):= first(svd(A))$
cond_2(A):= first(svd(A))/last(svd(A));
Of course, there may be more efficient ways to do the 2-norms and
2-cond numbers, but these work for me.
-sen
On Thu, 16 Aug 2007, Barton Willis wrote:
> -----sen1 at math.msu.edu wrote: -----
>
>> To: Barton Willis <willisb at unk.edu>
>> From: sen1 at math.msu.edu
>> Date: 08/16/2007 06:50AM
>> cc: maxima at math.utexas.edu
>> Subject: Re: [Maxima] printing in eigens_by_jacobi
>>
>> Thanks Barton,
>> BTW, is there a reason why the 2-norm is not an option for mat_norm?
>
> Sloth -- but the 2-norm for a non-numeric matrix is unlikely to
> be useful even in those rare cases when it is algebraic. My primary
> interest
> for linearalgebra was symbolic not numerical calculations.
>
>> Also, since there you have included the Jacobi algorithm, why not also
>> put in singular values? E.g. a function like svd(A) for a matrix A as
>> in octave.
>
> Don't we have that via translation of lapack? I know Ray added some stuff
> earlier this year -- I haven't used it yet.
>
> Barton
> _______________________________________________
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> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima
>
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