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Search results for: complex root finding
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Complex Root Finding Algorithm Based on Delaunay Triangulation
PublicationA simple and flexible algorithm for finding zeros of a complex function is presented. An arbitrary-shaped search region can be considered and a very wide class of functions can be analyzed, including those containing singular points or even branch cuts. The proposed technique is based on sampling the function at nodes of a regular or a self-adaptive mesh and on the analysis of the function sign changes. As a result, a set of candidate points...
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Efficient Complex Root Finding Algorithm for Microwave and Optical Propagation Problems
PublicationArticle 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...
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Evaluation of propagation parameters of open guiding structures with the use of complex root finding algorithms
PublicationAn efficient complex root tracing algorithm is utilized for the investigation of electromagnetic wave propagation in open guiding structures. The dispersion characteristics of propagated and leaky waves are calculated for a couple of chosen waveguides. The efficiency of the root tracing algorithm is discuses and compared to a global root finding algorithm.
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On root finding algorithms for complex functions with branch cuts
PublicationA 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...
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Multipath Complex Root Tracing
PublicationThe problem of multipath root tracing is being addressed in this communication. The self-adaptive complex root tracing algorithm, which was previously utilized for the investigation of various propagation and radiation problems, is analyzed here for the cases when the traced characteristic bifurcates. A procedure of multiroute detection is proposed and demonstrated on the coaxially loaded cylindrical waveguide example.
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Efficient Complex Root Tracing Algorithm for Propagation and Radiation Problems
PublicationAn efficient complex root tracing algorithm for propagation and radiation problems is presented. The proposed approach is based on a discretization of Cauchy’s Argument Principle and its generalization to the C × R space. Moreover, an engagement of the tracing process with a global root finding algorithm recently presented in the literature is performed. In order to confirm a validity and efficiency of the proposed technique, a...
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Global Complex Roots and Poles Finding Algorithm in C × R Domain
PublicationAn 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 ⊂ C × R and...
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Self-Adaptive Mesh Generator for Global Complex Roots and Poles Finding Algorithm
PublicationIn 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...
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An Improvement of Global Complex Roots and Poles Finding Algorithm for Propagation and Radiation Problems
PublicationAn improvement of the recently developed global roots finding algorithm has been proposed. The modification allows to shorten the computational time by reducing the number of function calls. Moreover, both versions of the algorithms (standard and modified) have been tested for numerically defined functions obtained from spectral domain approach and field matching method. The tests have been performed for three simple microwave...
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A Self-Adaptive Complex Root Tracing Algorithm for the Analysis of Propagation and Radiation Problem
PublicationAn improved complex root tracing algorithm for radiation and propagation issues is proposed. The approach is based on a self-adaptive discretization of Cauchy’s argument principle for a C × R space and requires a reduced number of function calls in comparison to other procedures presented in the literature. A few different examples concerning propagation and radiation problems have been considered to verify the validity and efficiency...
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Global Complex Roots and Poles Finding Algorithm Based on Phase Analysis for Propagation and Radiation Problems
PublicationA flexible and effective algorithm for complex roots and poles finding is presented. A wide class of analytic functions can be analyzed, and any arbitrarily shaped search region can be considered. The method is very simple and intuitive. It is based on sampling a function at the nodes of a regular mesh, and on the analysis of the function phase. As a result, a set of candidate regions is created and then the roots/poles are verified...
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Multimodal Particle Swarm Optimization with Phase Analysis to Solve Complex Equations of Electromagnetic Analysis
PublicationIn this paper, a new meta-heuristic method of finding roots and poles of a complex function of a complex variable is presented. The algorithm combines an efficient space exploration provided by the particle swarm optimization (PSO) and the classification of root and pole occurrences based on the phase analysis of the complex function. The method initially generates two uniformly distributed populations of particles on the complex...
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Multimodal Genetic Algorithm with Phase Analysis to Solve Complex Equations of Electromagnetic Analysis
PublicationIn this contribution, a new genetic-algorithm-based method of finding roots and poles of a complex function of a complex variable is presented. The algorithm employs the phase analysis of the function to explore the complex plane with the use of the genetic algorithm. Hence, the candidate regions of root and pole occurrences are selected and verified with the use of discrete Cauchy's argument principle. The algorithm is evaluated...
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A New Approach to Stability Evaluation of Digital Filters
PublicationIn this paper, a new numerical method of evaluating digital filter stability is presented. This approach is based on novel root-finding algorithms at the complex plane using the Delaunay triangulation and Cauchy's Argument Principle. The presented algorithm locates unstable zeros of the characteristic equation with their multiplicities. The proposed method is generic and can be applied to a vast range of systems. Verification of...
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Numerical Test for Stability Evaluation of Discrete-Time Systems
PublicationIn this paper, a new numerical test for stability evaluation of discrete-time systems is presented. It is based on modern root-finding techniques at the complex plane employing the Delaunay triangulation and Cauchy's Argument Principle. The method evaluates if a system is stable and returns possible values and multiplicities of unstable zeros of the characteristic equation. For state-space discrete-time models, the developed test...
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Scattering and Propagation Analysis for the Multilayered Structures Based on Field Matching Technique
PublicationA semi-analytical method is employed to the analysis of scattering and guiding problems in multilayer dielectric structures. The approach allows to investigate objects with arbitrary convex cross section and is based on the direct field matching technique involving the usage of the field projection at the boundary on a fixed set of orthogonal basis functions. For the scattering problems the scattered field in the far zone is calculated...
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Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
PublicationIn this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained...
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Analysis of graphene multi-strip planar guiding structures with the use of spectral domain approach
PublicationSpectral domain approach is modified and used to analyze some simple structures containing graphene strips. The modification is simple and concerns the Green’s function only. Moreover, the method is combined with the recently published root finding algorithms, which significantly improve the efficiency of the analysis. The results obtained for a simple guiding structure is verified and the field displacement effect is confirmed.
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RECSYS CHALLENGE 2015: a BUY EVENT PREDICTION IN THE E-COMMERCE DOMAIN
PublicationIn this paper we present our approach to RecSys Challenge 2015. Given a set of e-commerce events, the task is to predict whether a user will buy something in the current session and, if yes, which of the item will be bought. We show that the data preparation and enrichment are very important in finding the solution for the challenge and that simple ideas and intuitions could lead to satisfactory results. We also show that simple...
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Evaluating Accuracy of Respiratory Rate Estimation from Super Resolved Thermal Imagery
PublicationNon-contact estimation of Respiratory Rate (RR) has revolutionized the process of establishing the measurement by surpassing some issues related to attaching sensors to a body, e.g. epidermal stripping, skin disruption and pain. In this study, we perform further experiments with image processing-based RR estimation by using various image enhancement algorithms. Specifically, we employ Super Resolution (SR) Deep Learning (DL) network...