[Maxima] mnewton

[Andrej Vodopivec]

The patch uses complexfield (which is the field of complex floating
point numbers of the type double). To support bigfloats other parts of
mnewton should also be modified, so I didn't do that (it wouldn't be
hard). I guess there could be a switch which would control which field
should be used.

Andrej

On 7/17/07, Barton Willis <willisb at unk.edu> wrote:
>
> -----maxima-bounces at math.utexas.edu wrote: -----
>
>
> >Does the linearalgebra package have switches to allow the calculations
> >to be done with arbitrarily large precision?
>
> Yes. The undocumented function 'linsolve_by_lu' solves a linear system
> using partial
> pivoting:
>
> (%i1) m : vandermonde_matrix([2,3,42])$
> (%i2) b : matrix([1],[1],[4])$
>
> Solve using rational arithmetic without partial pivoting;
>
> (%i3) linsolve_by_lu(m,b);
> (%o3) [matrix([263/260],[-1/104],[1/520]),false]
>
> Solve using double floats and partial pivoting; the second list member
> in (%o4) is an estimate for the matrix condition number (for rational
> arithmetic, the condition number doesn't matter -- thus the second
> member of (%o3) is false):
>
> (%i4) linsolve_by_lu(m,b,'floatfield);
> (%o4)
> [matrix([1.011538461538462],[-0.0096153846153846],[0.0019230769230769]),12628.03416666667]
>
>
> Same as (%i4), but use big floats:
>
> (%i5) linsolve_by_lu(m,b,'bigfloatfield),fpprec : 28;
> (%o5)
> [matrix([1.011538461538461538461538462b0],[-9.615384615384615384615384627
> b-3],[1.923076923076923076923076923b-3]),12628.03416666667]
>
> For other options, do ? lu_factor.  If somebody would like to document the
> function
> 'linsovle_by_lu,' go ahead and do so (please---so much has changed in the
> way we
> do documentation, I'm not sure I know how to do it. Another thing: right
> now I can't test
> changes to documentation either ).