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21st International Conference on Microwave, Radar and Wireless Communications (MIKON)

作者： Kowalczyk, Piotr Gdansk Univ Technol Fac Elect Telecommun & Informat Narutowicza 11-12 PL-80233 Gdansk Poland

ISBN: (纸本)9781509022144

Article relates to the use of innovative root finding algorithm (on a complex plane) to study propagation properties of microwave and optical waveguides. Problems of this type occur not only in the analysis of lossy structures, but also in the study of complex and leaky modes (radiation phenomena). The proposed algorithm is simple to implement and can be applied for functions with singularities and branch cuts in the complex plane (frequently occurring in these types of issues).

关键词： root finding algorithm propagation waveguides

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Efficient Complex root finding algorithm for Microwave and Optical Propagation Problems

Efficient Complex Root Finding Algorithm for Microwave and O...

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International Conference on Microwave, Radar and Wireless Communications

作者： Piotr Kowalczyk Faculty of Electronics Telecommunication and Informatics Gdask University of Technology

ISBN: (纸本)9781509022151

关键词： root finding algorithm Propagation Waveguides

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Self-Adaptive Mesh Generator for Global Complex roots and Poles finding algorithm

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 2023年第7期71卷 2854-2863页

作者： Dziedziewicz, Sebastian Warecka, Malgorzata Lech, Rafal Kowalczyk, Piotr Gdansk Univ Technol Fac Elect Telecommun & Informat Dept Microwave & Antenna Engn PL-80233 Gdansk Poland

In any global method of searching for roots and poles, increasing the number of samples increases the chances of finding them precisely in a given area. However, the global complex roots and poles finding algorithm (GRPF) (as one of the few) has direct control over the accuracy of the results. In addition, this algorithm has a simple condition for finding all roots and poles in a given area: it only requires a sufficiently dense initial grid. However, in practice, this requirement may turn out to be very difficult to implement. For a complex and sophisticated function, the use of a regular high-density mesh may be ineffective or even impossible due to limited computational resources. In this article, a method for creating a self-adaptive initial mesh for this algorithm is presented. The proposed solution uses gradient calculation to identify areas that require mesh refinement, including areas where a zero and a pole are in close proximity. The adaptive mesh allows for faster and more accurate analysis of functions with a much smaller number of samples. As shown in the numerical examples, this approach reduces the number of function calls by several orders of magnitude, and thus significantly reduces the computational time.

关键词： Complex zeros and poles graphene numerical computations root finding algorithm roots of complex equation self-adaptive mesh zero/pole analysis of microwave filters

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Global Complex roots and Poles finding algorithm in C x R Domain

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IEEE ACCESS 2023年 11卷 68809-68817页

作者： Dziedziewicz, Sebastian Warecka, Malgorzata Lech, Rafal Kowalczyk, Piotr Gdansk Univ Technol Fac Elect Telecommun & Informat PL-80233 Gdansk Poland

An algorithm to find the roots and poles of a complex function depending on two arguments (one complex and one real) is proposed. Such problems are common in many fields of science for instance in electromagnetism, acoustics, stability analyses, spectroscopy, optics, and elementary particle physics. The proposed technique belongs to the class of global algorithms, gives a full picture of solutions in a fixed region Omega subset of C x R and can be very useful for preliminary analysis of the problem. The roots and poles are represented as curves in this domain. It is an efficient alternative not only to the complex plane zero search algorithms (which require multiple calls for different values of an additional real parameter) but also to tracking algorithms. The developed technique is based on the generalized Cauchy Argument Principle and Delaunay triangulation in three-dimensional space. The usefulness and effectiveness of the method are demonstrated on several examples concerning the analysis of guides (Anti-Resonant Reflecting Acoustic Waveguide, coaxially loaded cylindrical waveguide, graphene transmission line) and a resonant structure (Fabry-Perot open resonator).

关键词： Complex zeros and poles numerical computations root finding algorithm roots of complex equation resonators waveguide structures

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A method for finding numerical solutions to Diophantine equations using Spiral Optimization algorithm with Clustering (SOAC)

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APPLIED SOFT COMPUTING 2023年 145卷

作者： Sumarti, Novriana Sidarto, Kuntjoro Adji Kania, Adhe Edriani, Tiara Shofi Aditya, Yudi Inst Teknol Bandung Ind & Financial Math Res Grp Ganesha 10 Bandung 40132 Indonesia Inst Teknol Bandung Math Master Study Program Ganesha 10 Bandung 40132 Indonesia Inst Teknol Bandung Computat Sci Master Study Program Ganesha 10 Bandung 40132 Indonesia

Diophantine equations are equations containing two or more unknowns, such that only the integer solutions are required. To find solutions of these equations numerically, we can be performed by solving an optimization problem using a metaheuristic method. In this paper, the Spiral Optimization algorithm with Clustering (SOAC) method is proposed to find solutions to Diophantine equations in the form of polynomial, exponential, and also linear and nonlinear systems of equations. In the implementation of the method on solving some existing benchmark problems, the goal of simulation is to find all solutions only in a single run and in a short period of time. Appropriate values of required parameters are selected during the simulation. Results shows satisfactory in solving four problems in polynomial equations, four problems in exponential equations, and three problems in systems of linear and nonlinear equations. In most of cases, the results yield the same with the analytical or numerical solutions in the reference papers, and in some cases the results give more solutions.& COPY;2023 Elsevier B.V. All rights reserved.

关键词： Polynomial and exponential Diophantine equations The Markoff-Hurwitz equation root finding algorithm Optimization

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A dynamical interval Newton method

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EUROPEAN JOURNAL OF CONTROL 2021年 59卷 290-300页

作者： Menini, Laura Possieri, Corrado Tornambe, Antonio Univ Roma Tor Vergata Dipartimento Ingn Ind I-00133 Rome Italy CNR IASI Ist Anal Sistemi Informat A Ruberti I-00185 Rome Italy Univ Roma Tor Vergata Dipartimento Ingn Civile & Ingn Informat I-00133 Rome Italy

In this paper, a dynamical interval Newton's method is proposed to solve systems of nonlinear equations. Differently from other interval techniques available in the literature, the proposed method is capable of determining the roots of vector-valued time-varying functions. The design is carried out by firstly proposing an interval Newton's method capable of determining the roots of a scalar time-varying function and then extending these results to the vector-valued case. If the function to be zeroed is polynomial, then it is shown how to couple the proposed scalar and vector Newton's methods to determine improved estimates of its roots. Examples of application of the proposed procedure to the inverse kinematics of a robotic manipulator and to the problem of designing an observer for a nonlinear system are reported. (c) 2020 European Control Association. Published by Elsevier Ltd. All rights reserved.

关键词： root finding algorithm Interval estimation Polynomial methods Robotic manipulators Observer design

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Stability of a Certain 2-Dimensional Map with Cobweb Diagram 16th

Stability of a Certain 2-Dimensional Map with Cobweb Diagram

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16th International Conference on Computational Science and Its Applications (ICCSA)

作者： Kapcak, Sinan Amer Univ Middle East Egaila Kuwait

ISBN: (纸本)9783319420851

In this paper, we investigate the following discrete-time map: x(n+1) = phi(yn), y(n+1) = psi(x(n)). We introduce a novel method to determine the stability of the given two-dimensional map by using a one-dimensional map. A cobweb-like diagram is also introduced in order to analyze the stability of the system. We show that the stability of a fixed point in cobweb diagram implies the stability in phase diagram for the given system. In addition, an application of the system to a non-hyperbolic fixed point is also given.

关键词： Discrete dynamical systems Isoclines Global stability Cobweb diagram root finding algorithm

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How to improve interpolation attack

How to improve interpolation attack

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Symposium on Cryptography and Information Security

作者： Kurosawa, K Iwata, T Duong, QV Ibaraki Univ Dept Comp & Informat Sci Hitachi Ibaraki 3168511 Japan Natl Inst Info & Com Tech Dept Informat & Network Syst Koganei Tokyo 1848795 Japan

In the key recovery variant of the interpolation attack, exhaustive search is required to find the last round key K-m. Therefore, this attack is almost impractical if the size of K-m is too large. In this paper, we show that K-m can be very efficiently obtained if F(K, x) can be approximated by a low degree polynomial g(x)(K) in K for any fixed x, where F is a round function of Feistel type block ciphers.

关键词： block cipher interpolation attack root finding algorithm resultant

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A polynomial factorization approach for the discrete time GI^X/G/1/K queue

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METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY 2004年第3期6卷 277-291页

作者： Linwong, P Kato, N Nemoto, Y Tohoku Univ Grad Sch Informat Sci Aoba Ku Sendai Miyagi 9808579 Japan

This paper proposes a polynomial factorization approach for queue length distribution of discrete time GI(x) /G/1 and GI(x) /G/1/K queues. They are analyzed by using a two-component state model at the arrival and departure instants of customers. The equilibrium state-transition equations of state probabilities are solved by a polynomial factorization method. Finally, the queue length distributions are then obtained as linear combinations of geometric series, whose parameters are evaluated from roots of a characteristic polynomial.

关键词： discrete time GI(X)/G/1/K root finding algorithm queue length distribution

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Numerical factorization of a polynomial by rational Hermite interpolation

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Numerical algorithms 1992年第1期3卷 411-418页

作者： Sakurai, Tetsuya Sugiura, Hiroshi Torii, Tatsuo Department of Information Engineering Nagoya University Nagoya 464-01 Japan

We derive a class of iterative formulae to find numerically a factor of arbitrary degree of a polynomial f(x) based on the rational Hermite interpolation. The iterative formula generates the sequence of polynomials which converge to a factor of f(x). It has a high convergence order even for a factor which includes multiple zeros. Some numerical examples are also included. © 1992, J.C. Baltzer A.G. Scientific Publishing Company. All rights reserved.

关键词： algebraic equation AMS (MOS) Primary: 65D15 Euclidean algorithm numerical factorization Rational Hermite interpolant root finding algorithm Secondary: 65H05

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