On Halley iteration
In contrast to the Newton iteration, the Halley iteration formula contains an additional term in the denominator which increases the order by 1. There is also a modification for multiple roots. The investigations center around an analogy to the Newton-Kantorovich theorem. Moreover, the modification for \(m\)-fold roots does not shoot over \(m\) zeros in the real case.
scientific article; zbMATH DE number 1271908