查看更多>>摘要：Suppose that a system is affected by a sequence of shocks that occur randomly over time, and delta(1), delta(2), eta(1) and eta(2) are critical levels such that 0 < delta(1) < delta(2) and 0 < eta(1) < eta(2). In this paper, a new mixed delta-shock model is introduced for which the system fails with a probability, say theta(1), when the time between two consecutive shocks is lying in [delta(1), delta(2)], and the system fails with a probability, say theta(2), when the magnitude of a shock is lying in [eta(1), eta(2)]. The system fails with probability 1, as soon as the interarrival time between two successive shocks is less than delta(1) or a shock with magnitude greater than eta(2) occurs. The corresponding survival function is derived under two scenarios of independence and dependence between the interarrival times and the magnitude of shocks. The first and second moments are also derived. To illustrate the behavior of the system's lifetime, a simulation study is also conducted. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This foreword to the Virtual Special Issue dedicated to Luc Wuytack contains some historical information related to the founding of Journal CAM as well as to Luc's memory. It also serves as a preface to the collection of articles that have been selected to exemplify the field to which Luc devoted his career and around which the development of the journal CAM started. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：The Liu-type estimator has been consistently demonstrated to be an attractive shrinkage method to reduce the effect of multicollinearity problem. It is known that multicollinear-ity affects the variance of the maximum likelihood estimator negatively in gamma regression model. Therefore, an almost unbiased Liu-type estimator together with a modified version of it is proposed to overcome the multicollinearity problem. The performance of the new estimators is investigated both theoretically and numerically via a Monte Carlo simulation experiment and a real data illustration. Based on the results, it is observed that the proposed estimators can bring significant improvement relative to other competitor estimators. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Following the philosophy of the block Kaczmarz methods, we propose a randomized block Kaczmarz method with the blocks determined by the k-means clustering (RBK(k)). It can be considered as an efficient variant of the relaxed greedy randomized Kaczmarz algorithm by using a practical probability criterion for selecting the working block submatrix per iteration. The new algorithm is proved to be convergent when the linear system is consistent. A practical variant of the new method is also given. Some numerical examples are given to verify the effectiveness of the proposed methods. (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：The pattern (k(1), k(2), ... , k(l)) is defined to have at least k(1) consecutive 1's followed by at least k(2) consecutive 2's, ... , followed by at least k(l) consecutive l's. By iteratively applying the method that was developed previously to decouple the combinatorial complexity involved in studying complicated patterns in random sequences, the distribution of pattern (k(1), k(2), ... , k(l)) is derived for arbitrary e. Numerical examples are provided to illustrate the results. (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：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.
Bortoloti, M. A. A.Fernandes, T. A.Ferreira, O. P.
15页
查看更多>>摘要：We propose a new globalization strategy of the damped Newton method for finding singularities of a vector field on Riemannian manifolds. We establish its global convergence with a superlinear rate. In particular, this globalization generalizes the known damped Newton's method for general retraction. The global convergence analysis presented here does not require any hypothesis regarding a singularity of the vector field. We applied the proposed method to solve the truncated singular value problem on the product of two Stiefel manifolds, the dextrous hand grasping problem and an academic problem on the cone of symmetric positive definite matrices, the Rayleigh quotient and a problem of finding zeros of a non-conservative vector field on the sphere. Numerical experiments are presented, showing that the proposed algorithm is more robust than the known damped Newton's method. Published by Elsevier B.V.
查看更多>>摘要：A time-consistent evaluation is a dynamic pricing method according to which a risk that will be almost surely cheaper than another one at a future date should already be cheaper today. Common actuarial pricing approaches are usually not time-consistent. Pelsser and Ghalehjooghi (2016) derived time-consistent valuation principles from time inconsistent ones. The aim of this paper is twofold. Firstly, we propose a model for credit insurance portfolios taking into account the contagion risk via self-exciting jump processes. Secondly, we extend the approach of Pelsser and Ghalehjooghi to credit insurance in this framework. Starting from classical time-inconsistent actuarial pricing methods, we derive partial integro-differential equations (PIDE) for their time consistent counterparts. We discuss numerical methods for solving these PIDEs and their results. We draw two conclusions from these results. On the one hand, we show that time-consistent evaluations tend to give higher prices, compared to time-inconsistent evaluations. On the other hand, our results show that the time-consistency of evaluations allows to better take into account the risk of contagion in credit insurance, if such a risk exists. Finally, we propose a method to calibrate our model and use it in practice. (c) 2021 Elsevier B.V. All rights reserved.
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