查看更多>>摘要：In this manuscript, we design an efficient sixth-order scheme for solving nonlinear systems of equations, with only two steps in its iterative expression. Moreover, it belongs to a new parametric class of methods whose order of convergence is, at least, four. In this family, the most stable members have been selected by using techniques of real multidimensional dynamics; also, some members with undesirable chaotic behavior have been found and rejected for practical purposes. Finally, all these high-order schemes have been numerically checked and compared with other existing procedures of the same order of convergence, showing good and stable performance. (C) 2020 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this study, we obtain another representation of a relatively new method for solving the eigenvalue problem of the Frobenius companion matrix. We show that the iterative scheme under consideration is equivalent to the Weierstrass method. Based on this dependence, we derive new proofs of some known results and get new theoretical properties for the Weierstrass method. (C) 2021 Elsevier B.V. All rights reserved.
van der Meer, Remco W.Oosterlee, CornelisBorovykh, Anastasia
18页
查看更多>>摘要：Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks (Raissi et al., 2007). We introduce a generalization for these methods that manifests as a scaling parameter which balances the relative importance of the different constraints imposed by partial differential equations. A mathematical motivation of these generalized methods is provided, which shows that for linear and well-posed partial differential equations, the functional form is convex. We then derive a choice for the scaling parameter that is optimal with respect to a measure of relative error. Because this optimal choice relies on having full knowledge of analytical solutions, we also propose a heuristic method to approximate this optimal choice. The proposed methods are compared numerically to the original methods on a variety of model partial differential equations, with the number of data points being updated adaptively. For several problems, including high-dimensional PDEs the proposed methods are shown to significantly enhance accuracy. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：New calibrated estimators of quantiles and poverty measures are proposed. These estimators combine the incorporation of auxiliary information provided by auxiliary variables related to the variable of interest by calibration techniques with the selection of optimal calibration points under simple random sampling without replacement. The problem of selecting calibration points that minimize the asymptotic variance of the quantile estimator is addressed. Once the problem is solved, the definition of the new quantile estimator requires that the optimal estimator of the distribution function on which it is based verifies the properties of the distribution function. Through a theorem, the nondecreasing monotony property for the optimal estimator of the distribution function is established and the corresponding optimal estimator can be defined. This optimal quantile estimator is also used to define new estimators for poverty measures. Simulation studies with real data from the Spanish living conditions survey compares the performance of the new estimators against various methods proposed previously, where some resampling techniques are used for the variance estimation. Based on the results of the simulation study, the proposed estimators show a good performance and are a reasonable alternative to other estimators. (C) 2020 Elsevier B.V. All rights reserved.
查看更多>>摘要：In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to harness the notorious curse of dimensionality. The main forms of tensor decomposition include CP decomposition, Tucker decomposition, tensor train (TT) decomposition, etc. Each of the existing TT decomposition algorithms, including the TT-SVD and randomized TT-SVD, is successful in the field, but neither can both accurately and efficiently decompose large-scale sparse tensors. Based on previous research, this paper proposes a new quasi optimal fast TT decomposition algorithm for large-scale sparse tensors with proven correctness and the upper bound of computational complexity derived. It can also efficiently produce sparse TT with no numerical error and slightly larger TT-ranks on demand. In numerical experiments, we verify that the proposed algorithm can decompose sparse tensors in a much faster speed than the TT-SVD, and have advantages on speed, precision and versatility over the randomized TT-SVD and TT-cross. And, with it we can realize large-scale sparse matrix TT decomposition that was previously unachievable, enabling the tensor decomposition based algorithms to be applied in more scenarios. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Africa has long been ignored with respect to among others insurance modeling. In this paper, we propose a model for automobile claim data from Ghana. The body of the data are modeled by a lognormal distribution. However, the tail is noted be too heavy to be modeled by a single heavy tailed distribution. A mixture of distributions is used to model the tail. Estimates of risk are given. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In the analysis of the fluid queues, it is necessary to obtain the nonnegative solution of a nonsymmetric algebraic Riccati matrix equation. Under suitable conditions, this solution can be obtained transforming algebraic Riccati equations into unilateral quadratic matrix equations. In this paper, we use an efficient iterative scheme to approximate a solution of this quadratic matrix equation. We improve the efficiency and the accuracy of Newton's method, widely used in the literature. Moreover, a local convergence result is proved. Finally, we apply this efficient method to approximate the solution of a particular noisy Wiener-Hopf problem and we compare it with Newton's method. Moreover, a predictor- corrector iterative scheme is constructed that improve the accessibility of the aforesaid method.(c) 2020 Elsevier B.V. All rights reserved.
查看更多>>摘要：We construct in this paper a fully-decoupled and second-order accurate numerical scheme for solving the Cahn-Hilliard-Navier-Stokes phase-field model of two-phase incompressible flows. A full decoupling method is used by introducing several nonlocal variables and their ordinary differential equation to deal with the nonlinear and coupling terms. By combining with some effective methods to handle the Navier-Stokes equation, we obtain an efficient and easy-to-implement numerical scheme in which one only needs to solve several fully-decoupled linear elliptic equations with constant coefficients at each time step. We further prove the unconditional energy stability and solvability rigorously, and present various numerical simulations in 2D and 3D to demonstrate the efficiency and stability of the proposed scheme, numerically. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：A sequential quadratic hamiltonian (SQH) algorithm for solving nonsmooth supervised learning problems (SLPs) in the framework of residual neural networks is presented. In this framework, a SLP is interpreted as an optimal control problem and the SQH algorithm determines a solution using the characterization of optimality given by a discrete version of the Pontryagin maximum principle. Convergence and stability of the proposed algorithm is investigated theoretically in the framework of residual neural networks with Runge-Kutta structure, and its computational performance is compared to that of the so-called extended method of successive approximations. Results of numerical experiments demonstrate the superior performance of the SQH algorithm in terms of efficiency and robustness of the training process. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we investigate a direct and an inverse eigenvalue problem to recover doubly periodic pseudo-Jacobi matrices from three spectra lambda, mu(1), mu(2) and two positive numbers beta*, beta<>. Necessary and sufficient conditions for the existence of solution are given and numerical algorithms, using a modified unsymmetric Lanczos scheme, to reconstruct the matrix from the prescribed data are proposed. Some illustrative numerical examples are presented. The obtained results recover and extend several existing results in the literature.(c) 2021 Elsevier B.V. All rights reserved.
NSTL
Elsevier