Journal Article10.1109/22.210241
On the use of Davidenko's method in complex root search
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TL;DR: Davidenko's method has proved to be a powerful technique for solving a system of n-coupled nonlinear algebraic equations as discussed by the authors, which relaxes the restrictions that the initial guess has to be very close to the solution.
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Abstract: Davidenko's method has proved to be a powerful technique for solving a system of n-coupled nonlinear algebraic equations. It uses a Newton's method reduction to produce n-coupled first-order differential equations in a dummy variable. The advantage it offers over Newton's method and other traditional methods such as Muller's method is that it relaxes the restrictions that the initial guess has to be very close to the solution. Two examples involving the search for complex roots are presented. Davidenko's method seems to converge to the roots for all the arbitrary initial guesses considered while Muller's method appears to fail for some cases. This suggests the use of Davidenko's method as an alternative to Muller's method when the later fails to converge or is slowly convergent. >
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Citations
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TL;DR: In this paper , a modified Davidenko method via normalization was proposed for solving DNEs with unknown derivatives, which converges in finite time regardless of additive noise, and theoretical guarantees and numerical examples of the proposed method are provided.
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Low-Frequency Vibrations of Saccharides Using Terahertz Time-Domain Spectroscopy and Ab-Initio Simulations
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TL;DR: In this paper, the authors have developed analytical techniques for designing metal waveguides that achieve tailored optical functionalities, which are applied in two design examples which address contemporary problems related to waveguiding at sub-wavelength and nanometer scales.
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