(PC-12xx~14xx) Aberth method

[robve]

Shown below is a basic performance comparison of Aberth to Weierstrass/Durand-Kerner using 24 polynomials, four of which have roots with multiplicities. The number of iterations to converge to the given tolerance is shown. The standard (std) Durand-Kerner may produce NaN for polynomials with roots with multiplicities or does not converge. The improved/optimized C version (WDK) of Weierstrass/Durand-Kerner almost always converges regardless. Note that the improved/optimized Aberth version of Durand-Kerner (ADK) generally converges slightly faster. Tighter tolerances may cause convergence to be slow (linear) or even fail when multiplicities are present, a known weakness of Durand-Kerner. Quadruple precision may succeed to meet tighter tolerances (not shown).