mbeutel / quarticRootsFlocke

C++ rewrite of rpoly.f

quarticRootsFlocke

Polynomial Roots Solver

Port to C++ of Jenkins-Traub real polynomial root finder and the algorithm of Norbert Flocke for polynoms up to degree 4.

Doxygen documentation: http://ebertolazzi.github.io/quarticRootsFlocke/

Repository: https://github.com/ebertolazzi/quarticRootsFlocke

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.

References

• Algorithm 954: An Accurate and Efficient Cubic and Quartic Equation Solver for Physical Applications, ACM TOMS, vol 41, n.4, 2015

• A Three-Stage Algorithm for Real Polynomials Using Quadratic Iteration M. A. Jenkins and J. F. Traub 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: [e-mail]