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RPOLY - A Polynomial Root-finding library

A three-stage algorithm for finding roots of polynomials with real coefficients as outlined in: "A Three-Stage Algorithm for Real Polynomials Using Quadratic Iteration" by Jenkins and Traub, SIAM 1970. Please note that this variant is different than the complex-coefficient version, and is estimated to be up to 4 times faster.

The algorithm works by computing shifts in so-called "K-polynomials" that reveal the roots. These shifts are applied in three stages: Zero-shifts, Fixed-shifts, and Variable-shift iterations. Roots are revealed as real roots or as a pair of complex conjugate roots. After a root (or pair of roots) is found, it is divided from the polynomial and the process is repeated.


Eigen3 library:

This library is header-only so the installation is simple.


Run the following commands from the root directory of RpolyPlusPlus.

mkdir build
cd build
cmake ..

This should build the library. Note that the unit tests are enabled by default. To build without the unit tests change the cmake line to:

cmake .. -DBUILD_TESTING=Off

If testing is enabled, you can run the unit test from the build directory with:


All unit tests should pass.


Contact Chris Sweeney at