Paul's poptimal graph

By the way, Paul, I am terrifically impressed that you could
calculate enough points to draw a decent graph and find a minimum.
How in the world did you manage?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith <gwsmith@s...>"
<gwsmith@s...> wrote:
> By the way, Paul, I am terrifically impressed that you could
> calculate enough points to draw a decent graph and find a minimum.
> How in the world did you manage?

i have the matlab optimization toolbox. 1000 points took a few
seconds, probably less than 1 second had i used the 2.4 gigahertz
machine instead. i actually calculated 10000 points, taking a few
minutes, before plotting.

to find the minimum, i just minimized the function of p which
minimizes the p-norm of the errors (in the 5-limit). so i had to
write the first (logically, second) minimization as a matlab function
(1 line) and the second (logically, first) minimization as another
matlab function (4 lines) called by the first.

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus
<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith
<gwsmith@s...>"
> <gwsmith@s...> wrote:
> > By the way, Paul, I am terrifically impressed that you could
> > calculate enough points to draw a decent graph and find a
minimum.
> > How in the world did you manage?
>
> i have the matlab optimization toolbox. 1000 points took a few
> seconds, probably less than 1 second had i used the 2.4 gigahertz
> machine instead. i actually calculated 10000 points, taking a few
> minutes, before plotting.
>
> to find the minimum, i just minimized the function of p which
> minimizes the p-norm of the errors (in the 5-limit). so i had to
> write the first (logically, second) minimization as a matlab
function
> (1 line) and the second (logically, first) minimization as another
> matlab function (4 lines) called by the first.

I guess I should consider getting Matlab. Maple would take hours
getting even one of the points. Algebraically, using resultants and
Sturm sequences one can deal with the problem in another way, but it
is a huge mess involving high order polynomials.