Eigensolve
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
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
13
Compare with this image
Theory
number of components for given period