On root finding algorithms for complex functions with branch cuts

摘要

A simple and versatile method is presented, which enhances the complex root finding process by eliminating branch cuts and branch points in the analyzed domain. For any complex function defined by a finite number of Riemann sheets, a pointwise product of all the surfaces can be obtained. Such single-valued function is free of discontinuity caused by branch cuts and branch points. The roots of the new function are the same as the roots of original multi-valued variety, while the verification of them is much easier. Such approach can significantly improve the efficiency (as well as the effectiveness) of the root finding algorithms. The validity of the presented technique is supported by the results obtained from numerical tests.