Eigensolve :
- is a program by Steven Fortune that approximates the roots of a univariate polynomial.
- written in c++ for Linux
- it is a console application

How to install :

First install gmp, then eigensolve.

How to run :
Program needs an input file with coeficients of polynomial
# in console chage directory to eigensolve directory
# run and see results on the screen
./eigensolve wilk20.pol
# run and save results to the file
./eigensolve wilk20.pol >wilk20.txt
#run gnuplot
# plot data
plot "wilk20.txt"using 1:2 '(%lf,%lf)'
# Time of computing :

(time ./eigensolve data/cc1.pol > results/e_cc1.dat) 2>>results/E_time.txt

Example of use

8111 centers of hyperbolic components of Mandelbrot set for periods 1-13

1. input files (cc*.pol) were created with Maxima CAS script ( *.mac )
2. data files (cc*.dat) were created using eigensolve with use of input files ( cc*.pol)
./eigensolve cc1.pol >cc1.dat
3. image was made wih gnuplot using this batch script ( centers.plt)

period 13 ( degree 4095) - "it took two cpu days" Steve Fortune
period 14 ( degree 8127) - "I think each doubling of degree multiplies running time by 15 or so, so degree 8000 would be ~30 days cpu time." Steve Fortune

Comparison of MPSolve and Eigensolve :

# period #MPSolv #Eigensolve
1    0m0.003s
2    0m0.003s  0m0.008s
3    0m0.003s  0m0.008s
4    0m0.003s  0m0.009s
5    0m0.003s  0m0.025s
6   0m0.004s  0m0.061s
7    0m0.100s  0m0.156s
8    0m0.723s  0m0.689s
9    0m7.565s  0m7.124s
10  1m12.274s  1m5.324s
11   15m20.475s  13m43.406s
12  208m28.719s  149m0.718s

Compare with this image

number of components for given period