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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, JenkinsTraub, AbertEhrlich, DurandKerner, Ostrowski or Eigenvalue method. (Revised February 2017) 

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, JenkinsTraub, AberthEhrlich, DurandKerner, Ostrowski or the Eigenvalue method. Furthermore Newton's methods is represented using 4 different approaches: The Method by Madsen, The Method by GrantHitchins, Ostrowski method and the probably the most famous the method by JenkinsTraub (not really Newton, but the method start out using a simple Newton iteration until it closer to the root whereafter it shift to there fameous "A ThreeStage Algorithm for Real Polynominals using Quadratic Iteration". All 4 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, AberthEhrlich and DurandKerner 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. Ostrowski is a 4th order convergence method.


Methods for Polynomial with Real coefficients 
Methods for Polynomial with Complex coefficients 
 Newton by Madsen
 Newton by GrantHitchins
 Ostrowski
 JenkinsTraub
 DurandKerner
 Eigenvalue
 Bairstow
 Bairstow by Bond

 Newton by Madsen
 Newton by Grant Hitchins
 Ostrowski
 Laguerre
 Halley
 JenkinsTraub
 Graeffe by Malajovich
 DurandKerner
 AberthEhrlich

A multiprecision version (20200digits) 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 3.6 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 you can also download the RootFinder.exe without the installer.
Or try our web based polynomial roots or zero finder:
Web Solver

