Aledo, Juan A.Barzanouni, AliMalekbala, GhazalehSharifan, Leila...
13页
查看更多>>摘要：In this paper, we study the classical problems associated with fixed points in generalized parallel and sequential dynamical systems which are induced by a minterm or a maxterm Boolean function. In particular, we give a characterization of such fixed points which allows us to solve the fixed-point existence problem. Furthermore, we provide a method for counting the exact number of fixed points in such systems by means of a special kind of dominating sets. We demonstrate the main results for the case of generalized parallel dynamical systems induced by a minterm, what assure the same results in the case induced by maxterm thanks to the duality principle. In this context, the results are also valid for the sequential case, since the fixed points of any sequential system are the same of its parallel counterpart. These results generalize those given for parallel dynamical systems induced by such Boolean functions and also for normal AND-NOT networks (resp. OR-NOT networks) which are a particular case of generalized parallel dynamical systems induced by the minterm NOR (resp. maxterm NAND). (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In many studies in applied sciences and engineering one should find outer pseudo inverse of a matrix. In this paper, we propose a new efficient algorithm for computing the outer pseudo-inverse of a matrix. We study the convergence analysis of the new algorithm. Finally, test problems and simulation results support the theoretical approach. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper we extend the Residual Arnoldi method for calculating an extreme eigenvalue (e.g. largest real part, dominant, etc.) to the case where the matrices depend on parameters. The difference between this Arnoldi method and the classical Arnoldi algorithm is that in the former the residual is added to the subspace. We develop a Tensor-Krylov method that can be interpreted as an application of the Residual Arnoldi algorithm to a set of matrices obtained by evaluating a parameter-dependent matrix in parameter values on a grid. The subspace contains an approximate Krylov space for all these points. Instead of adding the residuals for all parameter values to the subspace we create a low-rank approximation of the matrix consisting of these residuals and add only the column space to the subspace. In order to keep the computations efficient, it is needed to limit the dimension of the subspace and to restart once the subspace has reached the prescribed maximal dimension. The novelty of this approach is twofold. Firstly, we observed that a large error in the low-rank approximations is allowed without slowing down the convergence, which implies that we can do more iterations before restarting. Secondly, we pay particular attention to the way the subspace is restarted, since classical restarting techniques give a too large subspace in our case. We motivate why it is good enough to just keep the approximation of the searched eigenvector. At the end of the paper we extend this algorithm to shift-and-invert Residual Arnoldi method to calculate the eigenvalue close to a shift & USigma; for a specific parameter dependency. We provide theoretical results and report numerical experiments. The Matlab code is publicly available. (C)& nbsp;2021 Published by Elsevier B.V.
查看更多>>摘要：In this paper, a gradually deteriorating system with imperfect repair is considered. The deterioration is modeled by a stationary stochastic process. The system fails once the deterioration level exceeds a given threshold L. At failure, an imperfect repair is performed and the deterioration level is reduced to a fixed value r, say. The system can be repaired n - 1 times and will be replaced after the nth failure. The article aims to estimate the parameters of the proposed deterioration process based on the observed failures. To this end we consider the Wiener and Gamma processes which are the most common used stochastic process models. In Wiener process, an explicit expression for the estimators is obtained. Birnbaum-Saunders approximation is extended to estimate the parameters in Gamma process. An optimal replacement policy is also discussed. Finally, a Monte-Carlo simulation is conducted to investigate the performance of estimators. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：The Newton-Raphson (N-R) method is one of the most ubiquitous approaches with several applications in numerous areas to find the optimization solution. It has long been known that in practice to apply the N-R method, it is customarily required to be obtained the second derivative of the objective function. Nevertheless, it is difficult or impossible to find the second derivative of the target function in many situations, leading to the impossibility to obtain the optimization solutions. This paper conducts a numerical method, develops an algorithm, and provides the R code so that one will be able to obtain the optimization solutions when our proposed approach is used. This study investigates numerous simulation studies and a factual data set. Based on the findings in this work, it can be firmly concluded that the N-R method with the numerical method for the second derivative of the objective function is found to be a robust and trustworthy approach. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：There are, currently, very few implementations to compute the hyperbolic cosine of a matrix. This work tries to fill this gap. To this end, we first introduce both a new rational-polynomial Hermite matrix expansion and a formula for the forward relative error of Hermite approximation in exact arithmetic with a sharp bound for the forward error. This matrix expansion allows obtaining a new accurate and efficient method for computing the hyperbolic matrix cosine. We present a MATLAB implementation, based on this method, which shows a superior efficiency and a better accuracy than other state -of-the-art methods. The algorithm developed on the basis of this method is also able to run on an NVIDIA GPU thanks to a MEX file that connects the MATLAB implementation to the CUDA code. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：A novel deficient complete quartic spline S having type II complete endpoint conditions S "(a) = f "(a) , S "(b) = f "(b) is constructed, with the expression given in the terms of the second derivative on the mesh nodes, and taking prescribed values on these grid nodes and at midpoints. The existence and uniqueness of this spline is proved, and the error estimates are provided. For less smooth interpolated functions, the interpolation error estimate is given in terms of the uniform modulus of continuity considering S "(a) = S "(b) = 0 as endpoint conditions. Two numerical examples illustrate the geometric properties of this deficient quartic spline interpolation operator. The error estimates are obtained for S, S', S ", and S "' showing an optimal order of convergence O(h(5)). (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper is concerned with the Kalman filtering problem for discrete-time linear systems corrupted by finite-step autocorrelated measurement noise which is a linear function of several mutually uncorrelated random vectors. An optimal Kalman filter is presented using state augment approach. Then, by new techniques developed in this paper, the convergence conditions of the optimal Kalman filter are established by equivalently considering the convergence of the prediction state error covariance of an augmented system where, different from the existing results, the matrix difference equation of the prediction augmented-state error covariance (PASEC) has a unique structure, that is, the matrix difference equation of the PASEC does not contain the measurement noise covariance and the process noise covariance of the augmented system in the equation is not positive definite. The main novelty of this paper is the theoretical analysis of the asymptotic convergence behavior of the PASEC whose matrix difference equation has the unique structure mentioned above. An example is presented to illustrate the effectiveness and advantages of the proposed new design strategy.(C) 2022 Elsevier B.V. All rights reserved.
Barakat, H. M.Mansour, G. M.Alawady, M. A.Husseiny, I. A....
16页
查看更多>>摘要：One of the most pliable and robust extensions of the classical FGM family of bivariate distributions is the Sarmanov family, which was proposed and used by Sarmanov (1974) as a new model of hydrological processes, inter alia. Despite the salient and almost unique features of this family, it is never used in the literature. The distribution theory of concomitants of record values from this family is investigated. Furthermore, the joint distribution of concomitants of record values for this family is studied. Besides, some aspects of information measures, namely, the Shannon entropy, inaccuracy measure, extropy, cumulative entropy, and Fisher information number are studied. Illustrative examples are provided, where numerical studies lend further support to the theoretical results. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We consider discrete penalized least-squares approximation on the unit sphere S-d, where the minimizer is sought in the space P-L(S-d) of spherical polynomials of degree <= L. The penalized least-squares functional is the sum of two terms both involving the weights and the nodes of a positive weight quadrature rule with polynomial degree of exactness at least 2L. The first one is a discrete least-squares functional measuring the squared weighted l(2) discrepancy between the noisy data and the approximation. The second term is the product of a regularization parameter lambda >= 0 times a penalization term that can be interpreted as an approximation of a squared semi-norm in the Sobolev (Hilbert) space H-s(S-d). The approximation can be computed directly via a summation process and does not require the solving of a linear system. For lambda = 0 (which is only appropriate if there is almost no noise), our approximation becomes a case of hyperinterpolation. As lambda > 0 increases, less weight is given to data fitting and more weight is given to keeping the approximation smooth. We derive L-2(S-d) error estimates for the approximation of functions from the Sobolev Hilbert space H-s(S-d), where s > d/2, from noisy data for the regularization parameter lambda chosen (i) as lambda = 0 (hyperinterpolation), (ii) for general lambda > 0, and (iii) with Morozov's discrepancy principle (an a posteriori parameter choice strategy). The L-2(S-d) error estimates in case (i) and (iii) are in a sense order-optimal. Numerical experiments explore the approximation method and illustrate the theoretical results. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
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Elsevier