Re: Roots of a multivariate polynomial



On 30 Jan., 12:27, hmob...@xxxxxxxxx wrote:
Hello,

I need help for finding a numerical algorithm to find a root of a
polynomial problem with the following characteristics:

1. Unlike common multivariate polynomial problems that appear as a
system of several equations, I only have ONE EQUATION, yet that single
equation is multivariate.

2. The algorithm should converge from any start point, because there
is NO inital GOOD GUESS about where solutions are.

3. There is no simple(isolated) root; so the algorithm must handle
MULTIPLICITIES greater than one

4. Only REAL roots are of interest.

5. Finding even ONE SOLUTION is sufficient.

6. Degree and number of varaibles are high (degree between 10-20 and
varaibles between 20-200).

Is there any algorithm for this purpose?

Regards

H.M.

Easy cases:
If the degree in any of the 20-200 variables is odd, things are easy:
Set all other variables to "random" values.
This should result in a polynomial in one variable with odd degree,
where finding a single root is easy.

Thus we have to assume that the degrees of all variables are even.
The top coefficient is a polynomial in one degree less.
If you can find a zero of that polynomial, you are back at the case of
odd degree.

More such tricks should be possible.

.

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