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Search results for: COMPLEX ROOTS FINDING ALGORITHM
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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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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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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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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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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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Testing Stability of Digital Filters Using Optimization Methods with Phase Analysis
PublicationIn this paper, novel methods for the evaluation of digital-filter stability are investigated. The methods are based on phase analysis of a complex function in the characteristic equation of a digital filter. It allows for evaluating stability when a characteristic equation is not based on a polynomial. The operation of these methods relies on sampling the unit circle on the complex plane and extracting the phase quadrant of a function...
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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...