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 use...
详细信息
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.
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 ...
详细信息
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.
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 rel...
详细信息
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.
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 undecida...
详细信息
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.
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...
详细信息
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.
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 m...
详细信息
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.
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 ...
详细信息
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.
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...
详细信息
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.
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 ...
详细信息
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.
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. Th...
详细信息
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.
暂无评论