Software that aims to provide an easy to use (hopefully) universal blackbox for solving polynomials and secular equations.
Among its features you can find:
- Arbitrary precision approximation.
- Guaranteed inclusion radii for the results.
- Exploiting of polynomial structures: it can take advantage of sparsity as well as coefficients in a particular domain (i.e. integers or rationals).
It can be specialized for specific classes of polynomials. As an example, see the roots of the Mandelbrot polynomial of degree 2.097.151 computed in about 10 days on a dual Xeon server.
If you use MPSolve in your research, please cite it as follows:
Bini, Dario A., Fiorentino, Giuseppe, Design, analysis, and implementation of a multiprecision polynomial rootfinder. Numerical Algorithms 23.2-3 (2000): 127-173.
Bini, Dario A., and Robol, Leonardo. Solving secular and polynomial equations: A multiprecision algorithm. Journal of Computational and Applied Mathematics 272 (2014): 276-292.
Found via
https://en.m.wikipedia.org/wiki/Aberth_method and
https://en.m.wikipedia.org/wiki/MPSolve
See also the GitHub repository
http://github.com/robol/MPSolve.git A simpler implementation of the Ehrich-Aberth-method can be found in
https://github.com/robol/ea-roots