Hello Barton,
you are right, there is are errors in the math text I am studying, whose caculation I
verify with Maxima:
Gramlich/Werner: Numerische Mathematik mit MatLab, 1.Ed. 2000, page 214.
I will send a mail to the authors ..
Sorry, I should have checked the calculation by my head :-)
so please excuse my sponaneous question and thanks for your help
HTH Wolfgang
"Barton Willis" <willisb at unk.edu> schrieb:
> ----maxima-bounces at math.utexas.edu wrote: -----
>
> >(%i1) load("linearalgebra");
> >(%i2) B: matrix([3,4],[4,5]);
> >(%i3) mat_cond(B,1); --> 84
> >(%i4) mat_cond(B,inf); --> 84
> >
> >which should be 24.
>
> Why 24? I get(with Maxima 5.11.0
>
> (%i1) load(linearalgebra)$
> (%i2) B: matrix([3,4],[4,5])$
> (%i3) mat_cond(B,1);
> (%o3) 81
> (%i4) mat_cond(B, 'inf);
> (%o4) 81
>
> I'm perplexed that you got 84 with Maxima 5.11.0. I also
> don't know why you expected 24 for the infinity norm.
>
> >I was surprised and calculated the matrix norm (which was also 'wrong')
>
> What did you get? What did you expect?
>
> (%i5) mat_norm(B,1);
> (%o5) 9
> (%i6) mat_norm(B,'inf);
> (%o6) 9
>
> Aren't these OK? row sum = 9 and column sum = 9.
>
> >and also
> >
> >(%i5) B^^-1; --> [ 5 -3]
> > [-4 3]
> >
> >which I expected to be 1/3* above.
>
> Why did you expect an additional factor of 1/3? I get
>
> (%i9) B^^-1;
> (%o9) matrix([-5,4],[4,-3])
> (%i10) %.B;
> (%o10) matrix([1,0],[0,1])
>
> Also the row and column sums of B^^-1 are 9. So the condition
> number is 81 for both the 1 and infinity norms.
>
> Barton