The Experts below are selected from a list of 32505 Experts worldwide ranked by ideXlab platform
Stoil Ivanov - One of the best experts on this subject based on the ideXlab platform.
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On the Convergence of Chebyshev’s Method for Multiple Polynomial Zeros
Results in Mathematics, 2015Co-Authors: Stoil IvanovAbstract:In this paper we investigate the local convergence of Chebyshev’s iterative method for the computation of a multiple Polynomial Zero. We establish two convergence theorems for Polynomials over an arbitrary normed field. A priori and a posteriori error estimates are also provided. All of the results are new even in the case of simple Zero.
Jun Wang - One of the best experts on this subject based on the ideXlab platform.
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New Implicit Enumeration Method for Polynomial 0-1 Programming
Systems Engineering - Theory & Practice, 2007Co-Authors: Jun WangAbstract:Abstract A new implicit enumeration method for Polynomial Zero-one programming is proposed in this article. By adopting the p-norm surrogate constraint method, a Polynomial Zero-one programming problem with multiple constraints can be converted into an equivalent Polynomial Zero-one programming problem with a single surrogate constraint. A new solution scheme is then devised to take the advantage of this prominent feature in carrying out the “fathoming” procedure and the “backtrack” procedure in a searching process of an implicit enumeration. We demonstrate the efficiency of this new algorithm by some promising computational results. Finally, we conclude by proposing certain topics for future research.
Umberto Viaro - One of the best experts on this subject based on the ideXlab platform.
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on Polynomial Zero exclusion from an rhp sector
International Conference on Methods and Models in Automation and Robotics, 2018Co-Authors: Daniele Casagrande, Wieslaw Krajewski, Umberto ViaroAbstract:Simple conditions based on generalisations of the Routh-Hurwitz and Mikhailov criteria that ensure the absence of Polynomial roots in an RHP sector straddling the positive real semi-axis ( $\mathcal{S}$ -stability) are presented. In particular, it is shown that $\mathcal{S}$ -stability is ensured if the phase variation of a suitable power of the original $n$ th-degree characteristic Polynomial is equal to $n\pi/2$ , which implies that the Zeros of the real and imaginary parts of this power must satisfy an interlacing property similar to the interlacing property satisfied by Hurwitz Polynomials according to the classic Hermite-Biehler theorem. The condition can be checked by means of Sturm sequences. Examples show how the proposed methods operate.
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MMAR - On Polynomial Zero Exclusion from an RHP Sector
2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR), 2018Co-Authors: Daniele Casagrande, Wieslaw Krajewski, Umberto ViaroAbstract:Simple conditions based on generalisations of the Routh-Hurwitz and Mikhailov criteria that ensure the absence of Polynomial roots in an RHP sector straddling the positive real semi-axis ( $\mathcal{S}$ -stability) are presented. In particular, it is shown that $\mathcal{S}$ -stability is ensured if the phase variation of a suitable power of the original $n$ th-degree characteristic Polynomial is equal to $n\pi/2$ , which implies that the Zeros of the real and imaginary parts of this power must satisfy an interlacing property similar to the interlacing property satisfied by Hurwitz Polynomials according to the classic Hermite-Biehler theorem. The condition can be checked by means of Sturm sequences. Examples show how the proposed methods operate.
Li Duan - One of the best experts on this subject based on the ideXlab platform.
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A New Implicit Enumeration Method for Polynomial 0-1 Programming and Applications
Systems Engineering - Theory & Practice, 2007Co-Authors: Li DuanAbstract:A new implicit enumeration method for Polynomial Zero-one programming is proposed in this paper.Adopting the p-norm surrogate constraint method,a Polynomial Zero-one programming problem with multiple constraints can be converted into an equivalent Polynomial Zero-one programming problem with a single surrogate constraint.A new solution scheme is then devised to take the advantage of this prominent feature in carrying out the "fathoming" procedure and the "backtrack" procedure in a searching process of an implicit enumeration.We demonstrate the efficiency of this new algorithm by computational results and also identify some new application areas.Finally,we conclude the paper by proposing some topics for future research.
Stoil I. Ivanov - One of the best experts on this subject based on the ideXlab platform.
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On the Convergence of Halley’s Method for Multiple Polynomial Zeros
Mediterranean Journal of Mathematics, 2014Co-Authors: Petko D. Proinov, Stoil I. IvanovAbstract:In this paper, we investigate the local convergence of Halley’s method for the computation of a multiple Polynomial Zero with known multiplicity. We establish two local convergence theorems for Halley’s method for multiple Polynomial Zeros under different initial conditions. The convergence of these results is cubic right from the first iteration. Also we find an initial condition which guarantees that an initial guess is an approximate Zero of the second kind for Halley’s method. All of the results are new even in the case of simple Zeros.