查看更多>>摘要：We study the analytical properties of the Laplace transform of the lognormal distribution. Two integral expressions for the analytic continuation of the Laplace transform of the lognormal distribution are provided, one of which takes the form of a Mellin-Barnes integral. As a corollary, we obtain an integral expression for the characteristic function. We present two approximations for the Laplace transform of the lognormal distribution, both valid in C \ (-infinity, 0]. In the last section, we discuss how one may use our results to compute the density of a sum of independent lognormal random variables. (C) 2021 Elsevier B.V. All rights reserved.
Moysi, A.Argyros, M.Argyros, I. K.Magrenan, a. A....
8页
查看更多>>摘要：In this work we are going to use the Kurchatov-Schmidt-Schwetlick-like solver (KSSLS) and the Kurchatov-like solver (KLS) to locate a zero, denoted by x* of operator F. We define F as F : D subset of & nbsp; B-1 -> B-2 where B-1 and B-2 stand for Banach spaces, D subset of B-1 be a convex set and F be a differentiable mapping according to Frechet. Under these conditions, for all n = 0, 1, 2, ... and 0 <=& nbsp;i <= m - 1 using Taylor expansion, KSSLS and KLS, when B-1 = B(2 )and high order derivatives and divided differences not appearing in these solvers, the results obtained are the restart of the utilization of these iterative solvers. Moreover, we show under the same set of conditions that the local convergence radii are the same, the uniqueness balls coincide but the error estimates on ||& nbsp;x(n) - x(*)|| differ. It is worth noticing our results improve the corresponding ones (Grau-Sanchez et al., 2011; Kurchatov, 1971 and Shakno, 2009). Finally, we apply our theoretical results to some numerical examples in order to prove the improvement. (C)(c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we propose an accelerated homotopy-perturbation-Kaczmarz iteration based on sequential subspace optimization method for solving nonlinear systems of inverse problems. The method is to iteratively project the initial value onto stripes the width of which are controlled by the search direction, the forward operator and the noise level to expedite the convergence. Under some general assumptions, we provide the convergence and regularization analysis for the proposed method. Finally, two numerical examples on inverse potential problems are presented to illustrate the effectiveness of reconstructing the solution and acceleration effect of the method. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we investigate the stability of a numerical method for solving the wave equation. The method uses explicit leap-frog in time and high order continuous and discontinuous (DG) finite elements using the standard Lagrange and Hermite basis functions in space. Matrix eigenvalue analysis is used to calculate time-step restrictions. We show that the time-step restriction for continuous Lagrange elements is independent of the nodal distribution, such as equidistributed Lagrange nodes and Gauss-Lobatto nodes. We show that the time-step restriction for the symmetric interior penalty DG schemes with the usual penalty terms is tighter than for continuous Lagrange finite elements. Finally, we conclude that the best time-step restriction is obtained for continuous Hermite finite elements up to polynomial degrees p = 13. (C) 2021 The Author(s). Published by Elsevier B.V.
Fernandez-Pendas, MarioCombarro, Elias F.Vallecorsa, SofiaRanilla, Jose...
17页
查看更多>>摘要：The Quantum Approximate Optimization Algorithm (QAOA) was proposed as a way of finding good, approximate solutions to hard combinatorial optimization problems. QAOA uses a hybrid approach. A parametrized quantum state is repeatedly prepared and measured on a quantum computer to estimate its average energy. Then, a classical optimizer, running in a classical computer, uses such information to decide on the new parameters that are then provided to the quantum computer. This process is iterated until some convergence criteria are met. Theoretically, almost all classical minimizers can be used in the hybrid scheme. However, their behaviour can vary greatly in both the quality of the final solution and the time they take to find it.& nbsp;In this work, we study the performance of twelve different classical optimizers when used with QAOA to solve the maximum cut problem in graphs. We conduct a thorough set of tests on a quantum simulator both, with and without noise, and present results that show that some optimizers can be hundreds of times more efficient than others in some cases. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we construct efficient collocation methods to deal with linear Volterra integral equations with highly oscillatory kernel. To discretize the oscillatory integrals in the collocation equation, a Filon type method is adopted. Based on some lemmas, we analyze the asymptotic property of the solution and obtain the convergence of the method, which is related to both the frequency omega and step length h. The proposed method does not only have the same order at the collocation points as the classical collocation method, but also may enjoy an asymptotic order which could reach two in some cases. Some numerical examples are presented at last to show the theoretical results and the efficiency of the method. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we use maximum principle preserving (MPP) and positivity-preserving (PP) parametrized flux limiters to achieve strict maximum principle and positivity-preserving property for the high order spectral volume (SV) scheme for solving hyperbolic conservation laws. This research is based on a generalization of the MPP and PP parametrized flux limiters in Xu (2014) and Christlieb et al. (2015) with Runge-Kutta (RK) time discretizations. For constructing MPP (PP) RK-SV schemes for hyperbolic conservation laws, we first focus on the RK-SV schemes to discuss how to apply MPP or PP parametrized flux limiters. Then we design and analyze high order MPP RK-SV schemes for scalar conservation laws, and high order PP RK-SV schemes for compressible Euler systems. The efficiency and effectiveness of the proposed schemes are demonstrated via a set of numerical experiments. Both the analysis and numerical experiments indicate that the proposed scheme without any additional time step restriction, not only preserves the maximum principle of the numerical approximation, but also maintains the designed high-order accuracy of the SV scheme for linear advection problems. (C) 2021 Published by Elsevier B.V.
查看更多>>摘要：In this paper we present a novel framework for obtaining high-order numerical methods for scalar conservation laws in one-space dimension for both the homogeneous and nonhomogeneous cases (or balance laws). The numerical schemes for these two settings are somewhat different in the presence of shocks, however at their core they both rely heavily on the solution curve being represented parametrically. By utilizing highorder parametric interpolation techniques we succeed to obtain fifth order accuracy (in space) everywhere in the computation domain, including the shock location itself. In the presence of source terms a slight modification is required, yet the spatial order is maintained but with an additional temporal error appearing. We provide a detailed discussion of a sample scheme for non-homogeneous problems which obtains fifth order in space and fourth order in time even in the presence of shocks. (C) 2021 Elsevier B.V. All rights reserved.
Ezquerro, J. A.Hernandez-Veron, M. A.Magrenan, a. A.
11页
查看更多>>摘要：We establish a global convergence result for an efficient third-order iterative process which is constructed from Chebyshev's method by approximating the second derivative of the operator involved by combinations of the operator. In particular, from the use of auxiliary points, we provide domains of restricted global convergence that allow obtaining balls of convergence and locate solutions. Finally, we use different numerical examples, including a Chandrashekar's integral equation problem, to illustrate the study. (C) 2021 The Authors. Published by Elsevier B.V.
Alba-Fernandez, M. V.Jimenez-Gamero, M. D.Jimenez-Jimenez, F.
13页
查看更多>>摘要：A test approach to the model selection problem for multinomial data based on penalized phi-divergences is proposed. The test statistic is a sample version of the difference of the distances between the population and each competing model. The null distribution of the test statistic is derived, showing that it depends on whether the competing models intersect or not and whether certain parameter is positive or not. All possible cases are characterized, and we give rules to decide if a model provides a better explanation for the available data than the other. The practical behavior of the proposal is evaluated by means of an extensive simulation experiment. The method is applied to a real data set related to the classification of individuals according to their social preferences. (C)& nbsp;2020 Elsevier B.V. All rights reserved.
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