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Permission to use, copy, and distribute this software and It’s documentation for any non commercial purpose is hereby granted without fee, provided: THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL Henrik Vestermark, BE LIABLE FOR ANY SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.

Root Finder finds all zeros (roots) of a polynomial of any degree with either real or complex coefficients using Bairstow's, Newton's, Halley's, Graeffe's, Laguerre's, Jenkins-Traub, Abert-Ehrlich, Durand-Kerner or Eigenvalue method.

RootFinder:
Finds all zeros (roots) of a polynomial of any degree with either real or complex coefficients using Bairstow's, Newton's, Halley's, Graeffe's, Laguerre's, Jenkins-Traub, Aberth-Ehrlich, Durand-Kerner or the Eigenvalue method. Furthermore Newton's methods is represented using 3 different approaches: The Method by Madsen, The Method by Grant-Hitchins and the probably the most famous the method by Jenkins-Traub. All 3 Newton variants existing in both a real coefficients and a complex coefficients version. Bairstow method can only handle real coefficients while Halley's, Graeffe's, Laguerre's, Aberth-Ehrlich and Durand-Kerner works on complex coefficients. Newton's method has quadratic convergence meaning that the number of significant digits double for each iterations while Halley's and Laguerre's has a cubic convergence meaning the number of significant digits tripe for each iterations.

Polynomials roots by Newton
Methods for Polynomial with Real coefficients Methods for Polynomial with Complex coefficients
  • Newton by Madsen
  • Newton by Grant-Hitchins
  • Jenkins-Traub
  • Durand-Kerner
  • Eigenvalue
  • Bairstow
  • Bairstow by Bond
  • Newton by Madsen
  • Newton by Grant Hitchins
  • Laguerre
  • Halley
  • Jenkins-Traub
  • Graeffe by Malajovich
  • Durand-Kerner
  • Aberth-Ehrlich
A multiprecision version (20-200digits) is also available.
A more detail analysis of each method is found in the user guide that can be downloaded directly from the link: Root Finder User Guide.

RootFinder version 3.3 now: (Complete rewritten version using Windows Form) Download (Windows Application. After installation the Rootfinder start automatically. RootFinder.exe will be installed in c:\Program Files\RootFinder).
Or try our web based polynomial roots or zero finder: Web Solver