查看更多>>摘要：As a widely used model, Mixture Density Model (MDM) is traditionally solved by Expectation-Maximization (EM) algorithm. EM maximizes a lower bound function iteratively, especially for exponential families. This paper managed to improve EM by combining it with Total Least Squares (TLS), proposing a new algorithm called the TLS-EM algorithm. In this algorithm, parameters are divided into two groups, linear parameters and sub-model parameters. They are solved in each iteration separately. First, data set is separated in different intervals and the conditional maximizing question is transformed into the over-determined linear equations. TLS is adopted to solve these equations and calculate linear parameters, with sub-model parameters fixed. Second, sub-model parameters are solved with EM. Properties of TLS-EM have been provided with proofs. Combining the properties of TLS, EM and the properties of its own, TLS-EM not only inherits most advantages of EM but also improves it in most cases, especially in bad initial or bad model conditions. Numerical experiments confirm these properties. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：The 2D-model of an elastic body with a finite set of rigid inclusions is considered. We assume that the body can come in frictionless contact on a part of its boundary with a rigid obstacle. On the remaining part of the body's boundary a homogeneous Dirichlet boundary condition is imposed. For a family of corresponding variational problems, we analyze the dependence of their solutions on locations of the rigid inclusions. Continuous dependency of the solutions on location parameters is established. The existence of a solution of the optimal control problem is proven. For this problem, a cost functional is defined by an arbitrary continuous functional on the solution space, while the control is given by location parameters of the rigid inclusions. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper develops a numerical two-level explicit approach for solving a mathematical model for the spread of Covid-19 pandemic with that includes the undetected infectious cases. The stability and convergence rate of the new numerical method are deeply analyzed in the L-infinity-norm. The proposed technique is less time consuming than a broad range of related numerical schemes. Furthermore, the method is stable, and at least second-order accurate and it can serve as a robust tool for the integration of general ODEs systems of initial-value problems. Some numerical experiments are provided which include the pandemic in Cameroon, and discussed. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We describe a stable and efficient algorithm for computing positive suboptimal extensions of the Gaussian quadrature rule with one or two degrees less of polynomial exactness than the corresponding Kronrod extension. These rules constitute a particular case of those first considered by Begumisa and Robinson (1991) and then by Patterson (1993) and have been proven to verify asymptotically good properties for a large class of weight functions. In particular, they may exist when the Gauss-Kronrod rule does not. The proposed algorithm is a nontrivial modification of the one introduced by Laurie (1997) for the Gauss-Kronrod quadrature, and it is based on the determination of an associated Jacobi matrix. The nodes and weights of the rule are then given as the eigenvalues and eigenvectors of the matrix, as in the classical Golub-Welsch algorithm (1969). (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In the current study, we provide a novel technique based on discrete shifted Hahn polynomials and Legendre-Gauss-Lobatto quadrature method for solving Caputo-Fabrizio fractional Volterra partial integro-differential equations (CFF-VPIDEs). The process of numerical algorithm contains the modified operational matrices (MOMs) and complement vectors (CVs), which directly influence the accuracy of the approach. Also, we expand the Volterra integral part of the equation with the help of the Legendre-Gauss- Lobatto quadrature method. The composition of the novel operational matrices with the Legendre-Gauss-Lobatto quadrature rule creates high precision and efficient method. Further, we present the error analysis of our scheme. Finally, to confirm the accuracy of theoretical results, we examine several examples. (c) 2021 Elsevier B.V. All rights reserved.
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