Improvements of the Modified Anderson-Björck (modAB) Root-Finding Algorithm

Modified Anderson-Björck’s method [1] is a new robust and efficient bracketing root finding algorithm. It combines bisection with Anderson-Björk’s method to achieve both fast performance and worst-case optimality. It relies on linearity check criteria for switching methods and uses Anderson-Björk corrections to overcome the fixed endpoint issue of false-position. Initial benchmarks of this method have shown certain performance advantages compared to other methods like Ridders, Brent and ITP. In this paper, we propose further improvements of the method and perform some additional analysis and benchmarks of its behavior and performance.