Determination of multiple roots of nonlinear equations and applications

作者：Hueso Jose L^*; Martinez Eulalia; Teruel Carles

来源：Journal of Mathematical Chemistry, 2015, 53(3): 880-892.

DOI：10.1007/s10910-014-0460-8

• Iterative methods
• Nonlinear equations
• Multiple roots
• Convergence order
• Efficiency

In this work we focus on the problem of approximating multiple roots of nonlinear equations. Multiple roots appear in some applications such as the compression of band-limited signals and the multipactor effect in electronic devices. We present a new family of iterative methods for multiple roots whose multiplicity is known. The methods are optimal in Kung-Traub's sense (Kung and Traub in J Assoc Comput Mach 21:643-651, [1]), because only three functional values per iteration are computed. By adding just one more function evaluation we make this family derivative free while preserving the convergence order. To check the theoretical results, we codify the new algorithms and apply them to different numerical examples.

• 出版日期2015-3