It is a well known fact that the algebraic as well as the geometric properties of complex holomorphic functions are not the same for their generalizations in quaternion analysis. In particular, because of the non-commutativity of quaternion multiplication, the use of root-finding methods involving iteration functions requires close attention.

In this talk we consider quaternion versions of Newton-like methods for finding roots of complex holomorphic functions, which can be successfully applied to special classes of quaternion valued functions.