On root finding algorithms for complex functions with branch cuts

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• 作者：Piotr Kowalczyk ^{pio.kow@gmail.com piotr.kowalczyk@pg.gda.pl}
• 关键词：Complex root finding ; Branch cuts ; Branch points
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：314
• 期：Complete
• 页码：1-9
• 全文大小：729 K
• 卷排序：314

文摘

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.