An extension to the analytical design of digital equiripple comb FIR filters is presented here. The filters are optimal in Chebyshev sense. The design runs from the filter specification through the degree formula to t...
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An extension to the analytical design of digital equiripple comb FIR filters is presented here. The filters are optimal in Chebyshev sense. The design runs from the filter specification through the degree formula to the impulse response coefficients, which are evaluated by an extremely efficient recursive algorithm. The proposed design method outperforms the standard procedures in terms of speed and robustness.
A simple and straightforward fast iterative method is presented for computing the inverse and determinant of any square matrix by successively applying order condensation and order expansion in an iterative process. A...
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A simple and straightforward fast iterative method is presented for computing the inverse and determinant of any square matrix by successively applying order condensation and order expansion in an iterative process. Applying the optimal iteration process, which comprises only some 20 lines of the MATLAB source code (using only simple elementary arithmetical operations), the inverse matrix can be computed within minutes from any given square matrix, even of relatively large size (such as 999), with real or complex entries, and irrespective of whether the matrix is singular or nonsingular.
This paper describes a class of networks called hierarchical networks and shows how reliability can be computed efficiently in a hierarchical network. In particular, it describes an algorithm for the K-terminal proble...
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This paper describes a class of networks called hierarchical networks and shows how reliability can be computed efficiently in a hierarchical network. In particular, it describes an algorithm for the K-terminal problem: computing the probability that a set of k nodes (k > 1) can communicate through the network. The algorithm complexity is polynomial with a small degree. The exact degree depends on the distribution of the nodes that desire to communicate and the external gateways.
algorithms have been available for exact performance evaluation of multi-state k-out-of-n systems. However, especially for complex systems with a large number of components, and a large number of possible states, obta...
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algorithms have been available for exact performance evaluation of multi-state k-out-of-n systems. However, especially for complex systems with a large number of components, and a large number of possible states, obtaining "reliability bounds" would be an interesting, significant issue. Reliability bounds will give us a range of the system reliability in a much shorter computation time, which allow us to make decisions more efficiently. The systems under consideration are multi-state k-out-of-n systems with i.i.d. components. We will focus on the probability of the system in states below a certain state d, denoted by Q(sd). Based on the recursive algorithm proposed by Zuo & Tian [14] for performance evaluation of multi-state k-out-of-n Systems with i.i.d. components, a reliability bounding approach is developed in this paper. The upper, and lower bounds of Q(sd) are,calculated by reducing the length of the k vector when using the recursive algorithm. Using the bounding approach, we can obtain a good estimate of the exact Q(sd) value while significantly reducing the computation time. This approach is attractive, especially to complex systems with a large number of components, and a large number of possible states. A numerical example is used to illustrate the significance of the proposed bounding approach.
The problem of parameter estimation when the data are corrupted by unknown but bounded errors mainly consists in characterizing the minimal parameter set consistent with the measurements, the model and the error descr...
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The problem of parameter estimation when the data are corrupted by unknown but bounded errors mainly consists in characterizing the minimal parameter set consistent with the measurements, the model and the error description. Two different approaches are reviewed and compared in this paper; the first one based on a recursive parameter ellipsoidal-bounding algorithm, the other on an orthotopic-bounding set, obtained by solving linear programming problems. The original ellipsoidal algorithm, modified for higher efficiency, has been compared with the linear programming method. Although the orthotopic description may result in a more accurately defined parameter region, it is time-consuming when a large number of measurements is present. Conversely, the ellipsodal-bounding algorithm often provides a loose approximation to the parameter region, but allows a fast data preprocessing, producing a smaller number of constraints that can be subsequently fed to the linear programming algorithm. A combined use of the two procedures is outlined and tested on simulated and real data, the latter being relative to the tuning of an A D converter, resulting in a remarkable reduction in the computing time.
As an important aspect of reliability theory, availability has now been considered a very meaningful design criterion of repairable system. This paper investigates the availability evaluation and design optimization o...
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As an important aspect of reliability theory, availability has now been considered a very meaningful design criterion of repairable system. This paper investigates the availability evaluation and design optimization of the multi-state k-out-of-n: G systems considering random weight threshold. The system availability is evaluated by extending the recursive algorithm (RA) and universal generating function (UGF) technique. Based on the traditional recursive algorithm, the total probability theorem is used to solve the discrete random weight threshold. Another better UGF method combines a new stochastic joint operator, which is suitable for both continuous and discrete random weight thresholds. Furthermore, we constructed two system design optimization models under availability or cost constraint respectively, and genetic algorithm (GA) programming can be applied to obtain the optimal state probability distribution and weight distribution of multi-state components of the suggested system. Finally, through numerical examples, the flexibility and effectiveness of the proposed methods for design optimization are demonstrated. In addition, two evaluation methods are compared to show that the customized UGF method features higher generality than RA in the case of continuous stochastic weight threshold, and higher operational efficiency in the case of increasing component quantity and state. The results can be helpful for engineers to optimize the design of complex systems.
The exact calculation of permanents of n x n matrices is a non-polynomial computational problem as a function of n. An efficient deterministic algorithm is presented that allows for the approximate calculation of perm...
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The exact calculation of permanents of n x n matrices is a non-polynomial computational problem as a function of n. An efficient deterministic algorithm is presented that allows for the approximate calculation of permanents obtained from sparse positive matrices within controllable precision bounds. The upper and lower bounds can be made arbitrarily close to each other and the algorithm outperforms existing ones for sufficiently large matrices. (C) 2002 Elsevier Science B.V. All rights reserved.
In this paper several recursive algorithms for computing M-estimates in multivariate linear regression models are discussed. It is shown that the recursive M-estimators of regression coefficient and scatter parameters...
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In this paper several recursive algorithms for computing M-estimates in multivariate linear regression models are discussed. It is shown that the recursive M-estimators of regression coefficient and scatter parameters are strongly consistent. In particular, the asymptotic normality of the recursive M-estimators regression coefficients is established. (C) 1996 Academic Press, Inc.
In system identification, the error evolution is composed of two decoupled parts: one is the identifying information on the current estimation residual, while the other is past arithmetic errors. Previous recursive al...
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In system identification, the error evolution is composed of two decoupled parts: one is the identifying information on the current estimation residual, while the other is past arithmetic errors. Previous recursive algorithms only considered how to update current prediction errors. Up to now, research has mostly been based on recursive least-squares (RLS) methods. In this note, a general recursive identification method is proposed for discrete systems. Using this new algorithm, a recursive empirical frequency-domain optimal parameter (REFOP) estimate is established. The REFOP method has the advantage of resisting disturbance noise. Some simulations are included to illustrate the new method's reliability.
In feature learning tasks, one of the most enormous challenges is to generate an efficient discriminative subspace. In this paper, we propose a novel subspace learning method, named recursive discriminative subspace l...
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In feature learning tasks, one of the most enormous challenges is to generate an efficient discriminative subspace. In this paper, we propose a novel subspace learning method, named recursive discriminative subspace learning with an l(1)-norm distance constraint (RDSL). RDSL can robustly extract features from the contaminated images and learn a discriminative subspace. With the use of an inequation-based l(1)-norm distance metric constraint, the minimized l(1)-norm distance metric objective function with slack variables induces samples in the same class to cluster as close as possible, meanwhile samples from different classes can be separated from each other as far as possible. By utilizing l(1)-norm items in both the objective function and the constraint, RDSL can well handle the noisy data and outliers. In addition, the large margin formulation makes the proposed method insensitive to initializations. We describe two approaches to solve RDSL with a recursive strategy. Experimental results on six benchmark datasets, including the original data and the contaminated data, demonstrate that RDSL outperforms the state-of-the-art methods.
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