Smale's alpha theory for certifiable numerical root finding.
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smale
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LICENSE
README.md

README.md

Smale

A collection of implementations of Smale's alpha theory for numerical root finding.

>>> from smale import smale_newton
>>> f = lambda x: x**3 - 1
>>> df = [lambda x: 3*x**2, lambda x: 6*x, lambda x: 6]
>>> smale_newton(f, 1.1, df)
1.0

Dependencies

Python Version

  • numpy
  • scipy
  • nosetests

C++ Version (coming soon)

Tests

Use nose at the top level directory to run tests:

$ cd path/to/smale
$ nosetests

ToDo

  • Implement C++11 version
  • Analytic continuation: given function of two (or more?) variables with one (or n-1?) treated as a parameter, numerically determine the variable as a function of the parameter(s).
  • Possible applications to dynamical systems, ODE solvers?