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An algebraic algorithm to isolate complex polynomial zeros using sturm sequences

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2000年第3-4期39卷 95-105页

作者： Brunetto, MAOC Claudio, DM Trevisan, V UEL Dept Comp BR-86051970 Londrina PR Brazil PUC RS Inst Matemat BR-90610001 Porto Alegre RS Brazil UFRGS Inst Matemat BR-91509900 Porto Alegre RS Brazil

In this paper, algorithms to enumerate and isolate complex polynomial roots are developed, analyzed,and implemented. We modified an algorithm due to Wilf, in which Sturm sequences and the principle of argument are used, by employing algebraic methods, aiming to enumerate zeros inside a rectangle in an exact way. Several improvements are introduced, such as dealing with zeros on the boundary of the rectangle. The performance of this new algorithm is evaluated in a theoretical as well as from a practical point of view, by means of experimental tests. The robustness of the algorithm is verified by using tests with ill-conditioned polynomials. We also compare the performance of this algorithm with the results of a recent paper, using different polynomial classes. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： polynomial zeros sturm sequences algebraic algorithm

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Double coupled canonical polyadic decomposition of third-order tensors: algebraic algorithm and relaxed uniqueness conditions

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SIGNAL PROCESSING-IMAGE COMMUNICATION 2019年 73卷 22-36页

作者： Gong, Xiao-Feng Lin, Qiu-Hua Cong, Feng-Yu De Lathauwer, Lieven Dalian Univ Technol Sch Informat & Commun Engn Dalian 116024 Peoples R China Dalian Univ Technol Dept Biomed Engn Dalian 116024 Peoples R China Katholieke Univ Leuven Dept Elect Engn ESAT STADIUS Ctr Dynam Syst Signal Proc & Data Analyt BE-3001 Leuven Belgium Katholieke Univ Leuven Grp Sci Engn & Technol B-8500 Kortrijk Belgium

Double coupled canonical polyadic decomposition (DC-CPD) decomposes multiple tensors with coupling in the first two modes, into minimal number of rank-1 tensors that also admit the double coupling structure. It has a particular interest in joint blind source separation (J-BSS) applications. In a preceding paper, we proposed an algebraic algorithm for underdetermined DC-CPD, of which the factor matrices in the first two modes of each tensor may have more columns than rows. It uses a pairwise coupled rank-1 detection mapping to transform a possibly underdetermined DC-CPD into an overdetermined DC-CPD, which can be solved algebraically via generalized eigenvalue decomposition (GEVD). In this paper, we generalize the pairwise or second-order coupled rank-1 detection mapping to an arbitrary order K >= 2. Based on this generalized coupled rank-1 detection mapping, we propose a broad framework for the algebraic computation of DC-CPD, which consists of a series of algorithms with more relaxed working assumptions, each corresponding to a fixed order K >= 2. Deterministic and generic uniqueness conditions are provided. We will show through analysis and numerical results that our new uniqueness conditions for DC-CPD are more relaxed than the existing results for DC-CPD and CPD. We will further show, through simulation results, the performance of the proposed algebraic DC-CPD framework in approximate DC-CPD and a J-BSS application, in comparison with existing DC-CPD and CPD algorithms.

关键词： Tensor Canonical polyadic decomposition Double coupled algebraic algorithm Uniqueness

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Single neuron PID adaptive control for BLDCM based on algebraic algorithm

Single neuron PID adaptive control for BLDCM based on algebr...

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2nd International Conference on Advanced Design and Manufacturing Engineering (ADME 2012)

作者： Diao, Yan Jia, Hongping Geng, Tianjun JiangSu Univ Sch Elect & Informat Engn Zhenjiang Peoples R China

ISBN: (纸本)9783037855034

The brushless DC motor control system often adopts the classic PID control, the advantages of which are as follows: simple to control, easy to adjust the parameter and a certain degree of control precision. But it relies on accurate mathematical model. The permanent magnet brushless DC motor control system is a multi-variable and nonlinear. As to the deficiencies of the classic PID control method, this thesis proposes a method called artificial neural network PID adaptive control method, which is based on algebraic algorithm and overcomes the shortcomings such as the slow convergence of BP algorithm, easy to trap in local minimum, and etc.

关键词： Artificial Neural Networks (ANN) single neuron algebraic algorithm PID control

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Characterisation of an algebraic algorithm for Probabilistic Automata 33

Characterisation of an Algebraic Algorithm for Probabilistic...

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33rd Symposium on Theoretical Aspects of Computer Science (STACS)

作者： Fijalkow, Nathanael Univ Oxford Oxford England LIAFA Paris 7 France Univ Warsaw Warsaw Poland

ISBN: (纸本)9783959770019

We consider the value 1 problem for probabilistic automata over finite words: it asks whether a given probabilistic automaton accepts words with probability arbitrarily close to 1. This problem is known to be undecidable. However, different algorithms have been proposed to partially solve it;it has been recently shown that the Markov Monoid algorithm, based on algebra, is the most correct algorithm so far. The first contribution of this paper is to give a characterisation of the Markov Monoid algorithm. The second contribution is to develop a profinite theory for probabilistic automata, called the prostochastic theory. This new framework gives a topological account of the value 1 problem, which in this context is cast as an emptiness problem. The above characterisation is reformulated using the prostochastic theory, allowing to give a modular proof.

关键词： Probabilistic Automata Value 1 Problem Markov Monoid algorithm algebraic algorithm Profinite Theory Topology in Computer Science

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Recursive Forward-Backward EDMD: Guaranteed algebraic Search for Koopman Invariant Subspaces

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IEEE ACCESS 2025年 13卷 61006-61025页

作者： Haseli, Masih Cortes, Jorge Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA

The implementation of the Koopman operator on digital computers often relies on the approximation of its action on finite-dimensional function spaces. This approximation is generally done by orthogonally projecting on the subspace. Extended Dynamic Mode Decomposition (EDMD) is a popular, special case of this projection procedure in a data-driven setting. Importantly, the accuracy of the model obtained by EDMD depends on the quality of the finite-dimensional space, specifically on how close it is to being invariant under the Koopman operator. This paper presents a data-driven algebraic search algorithm, termed Recursive Forward-Backward EDMD, for subspaces close to being invariant under the Koopman operator. Relying on the concept of temporal consistency, which measures the quality of the subspace, our algorithm recursively decomposes the search space into two subspaces with different prediction accuracy levels. The subspace with lower level of accuracy is removed if it does not reach a satisfactory threshold. The algorithm allows for tuning the level of accuracy depending on the underlying application and is endowed with convergence and accuracy guarantees.

关键词： Accuracy Eigenvalues and eigenfunctions Vectors Prediction algorithms Heuristic algorithms Hands Pollution measurement Complex systems Approximation algorithms Transmission line matrix methods Accuracy bound algebraic algorithm dynamic mode decomposition invariant subspace Koopman operator unknown nonlinear system

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algebraic algorithms for eigen-problems of a reduced biquaternion matrix and applications

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APPLIED MATHEMATICS AND COMPUTATION 2024年 463卷

作者： Guo, Zhenwei Jiang, Tongsong Wang, Gang Vasil'ev, V. I. North Eastern Fed Univ Inst Math & Informat Sci Yakutsk 677000 Russia Shandong Xiandai Univ Sch Elect Informat Jinan 250104 Shandong Peoples R China Linyi Univ Sch Math & Stat Linyi 276005 Peoples R China

In recent years, the reduced biquaternion algebras have been widely used in color image processing problems and in the field of electromagnetism. This paper studies eigen-problems of reduced biquaternion matrices by means of a complex representation of a reduced biquaternion matrix and derives new algebraic algorithms to find the eigenvalues and eigenvectors of reduced biquaternion matrices. This paper also concludes that the number of eigenvalues of an n x n reduced biquaternion matrix is infinite. In addition, the proposed algebraic algorithms are shown to be effective in application to a color face recognition problem.

关键词： Reduced biquaternion matrix Complex representation Eigenvalue Eigenvector algebraic algorithm

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algebraic algorithms for structure determination in biological chemistry

Algebraic algorithms for structure determination in biologic...

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Symposium on Mathematical Methods and Symbolic Calculation in Chemistry and Chemical Biology

作者： Emiris, IZ Fritzilas, ED Manocha, D Natl Univ Athens Dept Informat & Telecommun Athens 15784 Greece Natl Univ Athens Dept Biol Athens 15784 Greece Univ N Carolina Dept Comp Sci Chapel Hill NC 27599 USA

Several problems in computational chemistry, structural molecular biology, and biological chemistry can be solved by symbolic-numerical algorithms. We introduce suitable algebraic tools and then survey their usage in concrete applications. In particular, questions on molecular structure can be modeled by systems of polynomial equations, mainly by drawing on techniques from robot kinematics. Resultant-based algorithms, including sparse resultants and their matrix formulae, are described in order to reduce the solving of polynomial systems to numerical linear algebra. As an illustration, we focus on computing all conformations of cyclic molecules and on matching pharmacophores under distance constraints;in both cases, the number of independent degrees of freedom is relatively small. We summarize some existing results as well as sketch some original work. Both lead to complete and accurate solutions for those problems in the sense that our algorithms output all solutions with sufficiently high precision for the needs of biochemical applications. (c) 2005 Wiley Periodicals, Inc.

关键词： molecular conformation geometric constraint pharmacophore algebraic algorithm symbolic-numerical method

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algebraic nonuniformity correction algorithm based on Multiscale optical flow

Algebraic nonuniformity correction algorithm based on Multis...

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4th International Symposium on Photoelectronic Detection and Imaging (ISPDI) - Advances in Infrared Imaging and Applications

作者： He Ming Wang Xin-sai Wu Qiang Liu Yu Xu Hua-liang Guo Dong Air Def Forces Command Acad Lab Infrared & Imaging Nav Technol Zhengzhou 450052 Peoples R China

ISBN: (纸本)9780819488343

A multi-scale optical flow motion estimation based algorithm is developed for algebraic nonuniformity correction. First, the algorithm use time domain low pass filter filtering the random image frames noise. Then, use multi-scale optical flow estimation of the next frame. With these scene estimates and record frame, we can carry out nonuniformity correction. The strength of the algorithm lies in its good noise immunity, simple calculation and ability of real time processing. The fundamental and the flow of the proposed technique are described and the performance is demonstrated with infrared camera developed.

关键词： Infrared focal plane arrays multi-scale optical algebraic algorithm Bilinear interpolation Low-pass filter in time domain

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algebraic algorithms for structure determination in biological chemistry

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INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 2006年第1期106卷 190-210页

关键词： molecular conformation geometric constraint pharmacophore algebraic algorithm symbolic-numerical method

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A CLASS OF LINEAR-MAPS FOR ERROR CORRECTIVE DIMENSIONALITY REDUCTION OF BINARY TEMPLATES

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PATTERN RECOGNITION 1988年第4期21卷 381-392页

作者： KUNDU, S INDIAN STAT INST ELECTR & COMMUN SCI UNITCALCUTTA 700035W BENGALINDIA

Binary templates are optimally encoded in a reduced dimension by a proposed class of linear maps that preserves the local neighbourhood and a prescribed minimum distance between the prototypes to a workable extent. This in effect generates a nearness criterion suitable for template matching with a level of error correcting capability in the reduced space while requiring only a fraction of memory storage space and boolean operations that would have been required otherwise. Characters and symbols may now be designed with reference to separation and shape but with a comparative freedom from the constraint of dimension, while a volume of such data can be transmitted with the speed and bandwidth of the encoded data. Some of the principal problems associated with template matching are thus overcome. Here all the necessary operations are performed in the finite field GF(2) and the methodology developed can be implemented in a microcomputer with improved system performance and economy.

关键词： algebraic algorithm Dimensionality reduction Error correction Linear mapping Minimum distance encoding Neighbourhood preserving transformation Optimal encoding Probabilistic algorithm Perfect hash function Template stylization

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