Quartic Roots Solver

Polynomial Roots Solver

Port to C++ of the algorithm of Norbert Flocke for polynomial roots up to degree 4. Also Jenkins-Traub real polynomial root finder is ported but is experimental for the moment.

Usage

#include "PolynomialRoots.hh"

// ....

double coeffs[] = { 8, -8, 16,-16, 8,-8 }; // polynomial coeffs

double zeror[5], zeroi[5];
int    info[5];
int    degree = 5;

int ok = PolynomialRoots::roots( coeffs, degree, zeror, zeroi ); // ok < 0 failed
cout << " ok = " << ok << '\n' ;
for ( int i = 0 ; i < degree ; ++i )
  cout << zeror[i] << " + I* " << zeroi[i] << '\n';

To solve quadratic, cubic or quartic use specialized classes

Quadratic qsolve(a,b,c);
qsolve.info(cout);

Cubic csolve(a,b,c,d);
csolve.info(cout);

Quartic q4(a,b,c,d,e);
q4.info(cout);

look at the class definition to see how to access the computed roots.

Repository and Online Documentation

• https://github.com/ebertolazzi/quarticRootsFlocke
• http://ebertolazzi.github.io/quarticRootsFlocke

References

• N.Flocke

  Algorithm 954: An Accurate and Efficient Cubic and Quartic

  Equation Solver for Physical Applications

  ACM TOMS, vol 41, n.4, 2015
• M.A. Jenkins and J.F.Traub

  A Three-Stage Algorithm for Real Polynomials Using Quadratic Iteration

  SIAM Journal on Numerical Analysis

  Vol. 7, No. 4 (Dec., 1970), pp. 545-566

Author

Enrico Bertolazzi

Dipartimento di Ingegneria Industriale

Universita` degli Studi di Trento

email: enrico.bertolazzi@unitn.it