Re: [Maxima-discuss] solve() involving sqrt()

[Richard F. <fa...@cs...>]

I don't understand ... plugging those values in for x,y,z from minpack 
with starting point 1,1,1
gives rather large values,
e.g. eq1 is about 5.74. at the solution.

The results of solve (after appropriate squaring) from the solution I 
posed, gives results
like 10^(-10). ...
    [-5.474334493507415*10^-12,  3.548218062681546*10^-10, 
2.090438133731456*10^-9]


I assume more digits could be obtained by using a higher precision 
polynomial
zero-finder at the point in the algorithm that this system of equations 
is reduced to a polynomial
in one variable. But I sort of thought the answers would be good for a 
few decimal places.
I
I thought that feeding the results I found, namely

(%o24)  [x=3.857950974230044,y=4.622955406728833*10^-4,z=0.2397720333808264]

  into minpack  as a starting point, would result in about the same 
numbers returned..
  Instead resulted in the rather different set

(%o30) 
[[4.034938214233187,4.835038247043442*10^-4,0.2292547490241119],2.815769270875939*10^-15,1]

and when the 3 values for x,y,z were put back into eq1,2,3
the result was even better...

(%o31)    [-1.110223024625157*10^-15,  0.0, 2.58765558419226*10^-15]

Is this problem especially ill-conditioned?  one set looks like 
[3.8,4.6e-4,0.24]  the other [4,0, 4.8e-4, 0.23]
I did not expect them to differ in the 2nd or 3rd decimal place.

These answers are not particularly close to the results cited below, 
starting at 1,1,1.


RJF






On 9/14/2020 8:42 AM, Raymond Toy wrote:
>
>
> On Mon, Sep 14, 2020 at 8:32 AM Me Self <vla...@gm... 
> <mailto:vla...@gm...>> wrote:
>
>     > What starting points did you use?
>     >
>     > I got:
>     >
>     > minpack_solve([eq1,eq2,eq3],[x,y,z], [1,1,1]);
>     > Evaluation took 0.0100 seconds (0.0100 elapsed) using 942.305 KB.
>     >
>     > [[5.740409864561979,-1.755503737103853,0.1624466869294288],
>     >  0.01024886625263842,4]$
>
>     So do I, now. In fact, with a bit of tuning, it solves it just fine. I
>     think this happened because of the previous actions, I probably should
>     have used kill() before switching to minpack_solve(). I apologize for
>     the noise.
>
>
> If you can reproduce the issue, it would be nice to know; maybe some 
> check can be added to give a much better answer than just some random 
> lisp type error.
>
>
>
>     Regards,
>     Vlad
>
>
>
> -- 
> Ray
>
>
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