查看更多>>摘要：Iterative soft thresholding algorithm (ISTA) has a simple formulation and it can easily be implemented. Nevertheless, ISTA is limited to well-conditioned problems, e.g. compressive sensing. In this paper, we present an ISTA type algorithm based on the generalized conditional gradient method (GCGM) to solve elastic-net regularization which is commonly adopted in ill-conditioned problems. Furthermore, we propose a projected gradient (PG) method to accelerate the ISTA type algorithm. In addition, we discuss the existence of the radius R and we give a strategy to determine the radius R of the l1-ball constraint in the PG method by Morozov's discrepancy principle (MDP). Numerical results are reported to illustrate the efficiency of the proposed approach. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we consider the numerical approximations for the Cahn-Hilliard-Hele- Shaw system, which is a modified Cahn-Hilliard equation coupled with the Darcy flow law. One of challenges in solving this system numerically is how to develop linear discretization for the nonlinear term, while preserving the energy stability. By introduc-ing a Lagrange multiplier r, we construct a fully discrete, second-order linear scheme. The proposed scheme is rigorously proven to be uniquely solvable and unconditionally stable in energy. Moreover, we show theoretical analysis on error estimates of the time step size Tau and space step size h at the discrete level. Several numerical examples are presented to demonstrate the stability, accuracy and efficiency of the proposed scheme. We also show numerical simulations on the coarsening dynamics. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Anderson acceleration (AA) is a technique for accelerating the convergence of fixed-point iterations. In this paper, we apply AA to a sequence of functions and modify the norm in its internal optimization problem to the H-s norm, for some positive integer s, to bias it towards low-frequency spectral content in the residual. We analyze the convergence of AA by quantifying its improvement over Picard iteration. We find that AA based on the H-2 norm is well-suited to solve fixed-point operators derived from second-order elliptic differential operators, including the Helmholtz equation. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we focus on the spectra numerical computation for the integral equation with the absolute oscillation and power-law or logarithmic singularity. Finite section method is applied to transform the integral equation to an algebraic eigenvalue problem. The entries of the coefficient matrix appearing in the bivariate highly oscillatory singular integrals can be represented explicitly in Gamma or the exponential integral functions. The decay rate of the entries is established to construct the truncation scheme. Then the infinite algebraic eigenvalue problem can be simplified to be the finite one. The corresponding error of the infinite and finite algebraic systems is also bounded. Finally, the numerical experiments are provided to illustrate the theoretical analysis. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we derive a class of equivariant estimators of the directional parameter of the Watson distribution with a known concentration parameter. When all parameters are unknown, we derive restricted maximum likelihood estimators (MLEs) of the concentration parameters and Bayes estimators of the parameters under a noninformative prior. An improved likelihood ratio test is proposed to test equality of directional parameters of several Watson distributions with a common concentration parameter. We derive rules to classify axial data into one of the Watson populations on the hypersphere when all parameters are unknown. We propose classification rules based on the MLEs and the Bayes estimators of the parameters. The likelihood ratio-based rule, predictive Bayes rule, and kernel density classifier have been derived for two Watson populations. Moreover, the rules are compared using simulations. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems of polynomials. An important tool for this is the multivariate classical analysis of variance (ANOVA) decomposition. For functions with a low-dimensional structure, i.e., a low superposition dimension, we are able to achieve a reconstruction from scattered data and simultaneously understand relationships between different variables. (C) 2021 Elsevier B.V. All rights reserved.
Dinariev, O. YuRego, L. A. PessoaBedrikovetsky, P.
26页
查看更多>>摘要：This paper develops a modified version of the Boltzmann's equation for micro-scale particulate flow with capture and diffusion that describes the colloidal-suspension nano transport in porous media. An equivalent sink term is introduced into the kinetic equation instead of non-zero initial data, resulting in the solution of an operator equation in the Fourier space and an exact homogenization. The upper scale equation is obtained in closed form together with explicit formulae for the large-scale model coefficients in terms of the micro-scale parameters. The upscaling reveals the delay in particle transport if compared with the carrier water velocity, which is a collective effect of the particle capture and diffusion. The derived governing equation generalizes the current models for suspension-colloidal-nano transport in porous media. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper deals with the strong convergence and exponential stability of the stochastic theta (ST) method for stochastic differential equations with piecewise continuous arguments (SDEPCAs) with non-Lipschitzian and non-linear coefficients and mainly includes the following three results: (i) under the local Lipschitz and the monotone conditions, the ST method with theta is an element of [1/2, 1] is strongly convergent to SDEPCAs; (ii) the ST method with theta is an element of (1/2, 1] preserves the exponential mean square stability of SDEPCAs under the monotone condition and some conditions on the step-size; (iii) without any restriction on the step-size, there exists theta* is an element of (1/2, 1] such that the ST method with theta is an element of (theta*, 1] is exponentially stable in mean square. Moreover, for sufficiently small step-size, the rate constant can be reproduced. Some numerical simulations are provided to illustrate the theoretical results. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Nonlinear time-varying equation problems (NTVEPs), a core mathematical problem in engineering applications and scientific computing fields, have been widely researched in recent years. In this paper, the zeroing-dynamic design formula and continuous time Z-type model are revisited for solving NTVEPs. Then, a modified Z-type design formula is developed to address NTVEPs in the presence of noises. Specifically, a novel class of discrete-time noise-tolerant Z-type model with psi(tau)(chi(Tau), Tau) known (DTNTZTM-K) and discrete-time noise-tolerant Z-type model with psi(tau) (chi(Tau), Tau) unknown (DTNTZTMU) models are first proposed and investigated for online solving NTVEPs with different measurement noises. Furthermore, general-type DTNTZTM-K and DTNTZTM-U models (termed as GDTNTZTM-K and GDTNTZTM-U models) with different activation function are proposed to verify the robustness and superiority. In addition, theoretical analyses demonstrate that the presented DTNTZTM-K and DTNTZTM-U models are 0-stable, consistent and convergent. Besides, it further indicates that different activation functions can be utilized to accelerate the convergent speed of a class of general discrete-time noise-tolerant Z-type models, which demonstrates their high efficiency and robustness. Ultimately, numerical results show the efficacy and superiority of the proposed DTNTZTM-K, DTNTZTM-U, GDTNTZTM-K and GDTNTZTM-U models for noise-polluted NTVEPs compared with classical methods. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper discusses the finite element approximation of the Nikol'skij-Lizorkin problem with degeneracy on the entire boundary of the domain. The triangulation of the domain with a special compression of nodes to the boundary of the domain was carried out. It was established that the approximation to the exact solution has first-order convergence in the norm of the Sobolev weighted space W-2,alpha(1)(Omega) at special exponent of the degree of mesh compression. Numerical experiments confirmed the established estimate of the convergence rate. (c) 2021 Elsevier B.V. All rights reserved.
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