New Root-Seeking Algorithms

[ttw]

There are a couple of more root finders that I have used. One is Brents's algorithm (inverse quardratic interpolation with bisection) and the other is the "Illinois" algorithm (which I heard of long before the published work.) There is another modification of Newton's method that raises its effective rate (to Sqrt(8)). The idea is to evaluate f(x) and f'(x) at different xs. (http://www.sciencedirect.com/science/art...30)There's also Chebychev's method which is (like Halley's) a Taylor series; Chebychev used the series and Halley used the continued fraction for the series. Also a guy named Galindo did rather well with bunches of tests and algorithms.