Improved Aberth-Ehrlich root-finding algorithm and its further application for Binary Microlensing

ABSTRACT In gravitational microlensing formalism and for modelling binary light curves, the key step is solving lens equation. Currently, a combination of Newton’s Laguerre’s methods which was first introduced by Skowron & Gould (SG) used while curves. this paper, we introduce fast root-finding algorithm univariate polynomials based on Aberth–Ehrlich (AE) method developed in 1967 as an improvement over method. AE has proven to be much faster than Newton’s, Laguerre’s, Durand–Kerner unlike other algorithms, it able produce all roots simultaneously. After improving basic discussing its properties, will optimize equations, are fifth degree with complex coefficients. Our about 1.8–2.0 times SG algorithm. Since, calculating magnification factors point-like or finite source stars, necessary solve equation find positions produced images image plane first, new improve speed accuracy modelling.