查看更多>>摘要：We examine several of the normal-form multivariate polynomial rootfinding methods of Telen, Mourrain, and Van Barel and some variants of those methods. We analyze the performance of these variants in terms of their asymptotic temporal complexity as well as speed and accuracy on a wide range of numerical experiments. All variants of the algorithm are problematic for systems in which many roots are very close together. We analyze the performance on one such system in detail, namely the "devastating example "that Noferini and Townsend used to demonstrate instability of resultant-based methods. We demonstrate that the problems with the devastating example arise from having a large number of roots very close to each other. We also show that a small number of clustered roots does not cause numerical problems for these methods. We conjecture that the clustering of many roots is the primary source of problematic examples. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper presents a high order all-speed semi-implicit weighted compact nonlinear scheme (WCNS) for the isentropic Navier-Stokes system. To avoid the severe CFL stability restriction, the pressure and viscous terms are treated implicitly in time, while the other terms are treated explicitly in time. The third-order IMEX Runge- Kutta methods and the fifth-order WCNS are used for time discretization and spatial discretization, respectively. The generated linear equations of velocity components are solved by the GMRES iterative algorithm. Numerical results in one, two and three dimensions in both compressible and incompressible regimes are presented to show the performance of the designed scheme. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：The generalized inverse Gaussian (GIG) Levy process is a limit of compound Poisson processes, including the stationary gamma process and the stationary inverse Gaussian process as special cases. However, fitting the GIG Levy process to data is computationally intractable due to the fact that the marginal distribution of the GIG Levy process is not convolution-closed. The current work reveals that the marginal distribution of the GIG Levy process admits a simple yet extremely accurate saddlepoint approximation. Particularly, we prove that if the order parameter of the GIG distribution is greater than or equal to -1, the marginal distribution can be approximated accurately - no need to normalize the saddlepoint density. Accordingly, maximum likelihood estimation is simple and quick, random number generation from the marginal distribution is straight-forward by using Monte Carlo methods, and goodness-of-fit testing is undemanding to perform. Therefore, major numerical impediments to the application of the GIG Levy process are removed. We demonstrate the accuracy of the saddlepoint approximation via various experimental setups. (C)& nbsp;2022 The Author(s). Published by Elsevier B.V.
Noeiaghdam, SamadAraghi, Mohammad Ali FariborziSidorov, Denis
13页
查看更多>>摘要：In this research, an efficient scheme is presented to validate the numerical results and solve the second kind integral equations (IEs). For this reason the homotopy perturbation method (HPM) is illustrated and the stochastic arithmetic is applied to implement the CESTAC1 method for solving IEs. The accuracy of method is shown by proving a main theorem. Also, the CADNA2 library is used instead of other usual softwares. Applying the mentioned method, the optimal approximation, iteration, validation of results and any numerical instability can be found whereas the floating-point arithmetic (FPA) has not these properties. Some examples are solved to determine the significance of applying the SA in place of the FPA.
查看更多>>摘要：Assuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. With the sampling time step arbitrarily fixed, we prove the strong consistency and asymptotic normality of our estimators as the sample size tends to infinity. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：The error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier-Stokes equations is carried out. A grad-div stabilization term is added to the formulation of the POD method. Error bounds with constants independent on inverse powers of the viscosity parameter are derived for the POD algorithm. No upper bounds in the nudging parameter of the data assimilation method are required. Numerical experiments show that, for large values of the nudging parameter, the proposed method rapidly converges to the real solution, and greatly improves the overall accuracy of standard POD schemes up to low viscosities over predictive time intervals. (C) 2022 The Author(s). Published by Elsevier B.V.
查看更多>>摘要：Projection depth (PD), one of the prevailing location depth notions, is a powerful and favored tool for multivariate nonparametric analysis. It permits the extension of the univariate median and weighted means to a multivariate setting. The multidimensional projection depth median (PM) and depth weighted means, including the Stahel-Donoho (SD) estimator are highly robust and affine equivariant. PM has the highest finite sample breakdown point robustness among affine equivariant location estimators. However, the computation of PD remains a challenge because its exact computation is only feasible for a data set with a dimension that is theoretically no higher than eight but practically no higher than three. Approximate algorithms such as random direction procedure or simulated annealing (SA) algorithm, are time-consuming in high dimensional cases. Here, we present an efficient SA algorithm and its extension for the computation of PD. Simulated and real data examples indicate that the proposed algorithms outperform their competitors, including the Nelder-Mead method, and the SA algorithm, in high-dimensional cases and can obtain highly accurate results compared with those of the exact algorithm in low-dimensional cases.(C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We introduce a characterization for affine equivalence of two surfaces of translation defined by either rational or meromorphic generators. In turn, this induces a similar characterization for minimal surfaces. In the rational case, our results provide algorithms for detecting affine equivalence of these surfaces, and therefore, in particular, the symmetries of a surface of translation or a minimal surface of the considered types. Additionally, we apply our results to designing surfaces of translation and minimal surfaces with symmetries, and to computing the symmetries of the higher-order Enneper surfaces. (C) 2022 The Author(s). Published by Elsevier B.V.
查看更多>>摘要：This paper is concerned with an inverse problem of recovering the space-dependent advection coefficient and the fractional order in a one-dimensional time-fractional reaction-advection-diffusion-wave equation. Based on a transformation, the original equation can be changed into a new form without an advection term. Then we show the uniqueness of recovering the fractional order and the zeroth-order coefficient which contains the information of the "original "advection coefficient by the observation data at two end points. Under the theory of the first-order ordinary differential equation, we obtain the uniqueness result of the advection coefficient. Lastly, we solve the inverse problem numerically from Bayesian perspective by using the iterative regularizing ensemble Kalman method, and numerical examples are presented to show the effectiveness of the proposed method. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
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Elsevier