Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Solving cubics by polynomial fitting
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
A fast and highly accurate algorithm for solving quartic equations is introduced. This new algorithm is more than six times as fast and several times more accurate than the quasi-standard Companion matrix eigenvalue quartic solver. Moreover, the method is exceptionally robust in cases of extreme root spread. The new algorithm is based on a factorization of the quartic in two quadratics, which are solved in closed form. The performance key at this point is a fixed-point iteration based fitting algorithm for backward optimization of the underlying quartic-to-quadratic polynomial decomposition. Detailed experimental results confirm our claims.