查看更多>>摘要：In this paper, we present a new parallel accurate algorithm called PAccSumK for computing summation of floating-point numbers. It is based on AccSumK algorithm. In the experiment, for the summation problems with large condition numbers, our algorithm outperforms the PSumK algorithm in terms of accuracy and computing time. The reason is that our algorithm is based on a more accurate algorithm called AccSumK algorithm compared to the SumL algorithm used in PSumK. The proposed parallel algorithm in this paper is designed to compute a result as if computed internally in K-fold the working precision. Numerical results are presented showing the performance and the accuracy of our new parallel algorithm for calculating summation. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, the eigenvalue problem for the class of quasi-generalized Vandermonde (q-gV) matrices is considered. In order to parameterize q-gV matrices, the explicit expressions of minors of such matrices are presented. We develop an algorithm to accurately compute the parameterization for q-gV matrices. Relying on the accurate parameterization, all the eigenvalues of q-gV matrices are computed to high relative accuracy. Error analysis and numerical experiments are provided to confirm the high relative accuracy. (C)& nbsp;2021 Elsevier B.V. All rights reserved.& nbsp;
查看更多>>摘要：This paper focuses on the pricing of continuous geometric Asian options (GAOs) under a new multifactor stochastic volatility model. The model considers fast and slow mean reverting factors of volatility, where slow volatility factor is approximated by a quadratic arc. The asymptotic expansion of the price function is assumed, and the first order price approximation is derived using the perturbation techniques for both floating and fixed strike GAOs. Much simplified pricing formulae for the GAOs are obtained in this multifactor stochastic volatility framework. The zeroth order term in the price approximation is the modified Black-Scholes price for the GAOs. This modified price is expressed in terms of the Black-Scholes price for the GAOs. The accuracy of the approximate option pricing formulae is established, and also verified numerically by comparing the model prices with the Monte Carlo simulation prices and the Black- Scholes prices for the GAOs. The model parameter is estimated by capturing the volatility smiles. The sensitivity analysis is also performed to investigate the effect of underlying parameters on the approximated prices. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Starting from the matrix form of the fractional Cauchy problem, new formulae for the sum of the three-parameter Mittag-Leffler functions are deduced. The derivation is based on the Prabhakar fractional integral operator. A Volterra integral equation relating the solution of the Cauchy problem with that of a perturbed problem is also obtained; from this a condition number measuring the sensitivity of the solution to changes in data can be derived. Several examples are also incorporated to test the bounds. (c) 2021 Elsevier B.V. All rights reserved.
Kuczynski, M. D.Borchardt, M.Kleiber, R.Koenies, A....
8页
查看更多>>摘要：We present a Fourier-decomposition-based approach aided by a Neural Network for the classification of the eigenfunctions of an operator appearing in ideal magnetohydrodynamics. The Neural Network is trained on individual Fourier modes, which enhances the robustness of the classification. In our tests, the algorithm correctly classified 93.5% of the data and returned the remaining 6.5% for manual classification. The probability of misidentifying the eigenfunctions is estimated as 0.03%. The discussion is kept quite general allowing for potential applications in other fields. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This manuscript is devoted to studying approximations of a coupled Klein-Gordon-Zakharov system where different orders of fractional spatial derivatives are utilized. The fractional derivatives involved are in the Riesz sense. It is understood that such a modeling system possesses an energy functional which is conserved throughout the period of time considered, and that its solutions are uniformly bounded. Motivated by these facts, we propose two numerical models to approximate the underlying continuous system. While both approximations remain to be nonlinear, one of them is implicit and the other is explicit. For each of the discretized models, we introduce a proper discrete energy functional to estimate the total energy of the continuous system. We prove that such a discrete energy is conserved in both cases. The existence of solutions of the numerical models is established via fixed-point theorems. Continuing explorations of intrinsic properties of the numerical solutions are carried out. More specifically, we show rigorously that the two schemes constructed are capable of preserving the boundedness of the approximations and that they yield consistent estimates of the true solution. Numerical stability and convergence are likewise proved theoretically. As one of the consequences, the uniqueness of numerical solutions is shown rigorously for both discretized models. Finally, comparisons of the numerical solutions are provided, in order to evaluate the capabilities of these discrete methods to preserve the discrete energy of underlying systems. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper we design a family of fully implicit strong Ito-Taylor numerical methods for stochastic differential equations (SDE). These methods are based on the truncation of our general stochastic Ito-Taylor expansions, in which the truncation can be chosen to make our methods converge with high order. And by selecting the parameters in the methods, we can get methods with different stability. The mean-square (MS) stability of the second-order case is investigated. Numerical results are reported to show the convergence properties and the stability properties of our methods.(C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We show that the LSPIA method for curve and surface approximation, which was introduced by Deng and Lin (2014), is equivalent to a gradient descent method. We also note that Deng and Lin's results concerning feasible values of the stepsize are directly implied by classical results about convergence properties of the gradient descent method. We propose a modification based on stochastic gradient descent, which lends itself to a realization that employs the technology of neural networks. In addition, we show how to incorporate the optimization of the parameterization of the given data into this framework via parameter correction (PC). This leads to the new LSPIA-PC method and its neural-network based implementation. Numerical experiments indicate that it gives better results than LSPIA with comparable computational costs. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Numerical approximation of stochastic Stokes-Darcy equations usually requires repeated sampling of the random hydraulic conductivity tensor and then simulating flow ensembles. In this setting, we propose an efficient, second order, ensemble algorithm for fast computation of the whole set of realizations of the stochastic Stokes-Darcy model corresponding to different random hydraulic conductivity tensor samples. The ensemble algorithm only requires the solution of two linear systems that have the same constant coefficient matrices for all realizations. We give a complete long time stability and convergence analysis for the method. Numerical experiments are presented to support theoretical results and demonstrate the application of the method. (C)& nbsp;2021 Elsevier B.V. All rights reserved.& nbsp;
查看更多>>摘要：In this paper, we propose a recovery-type a posteriori error estimator of the weak Galerkin finite element method for the second order elliptic equation. The reliability and efficiency of the estimator are analyzed by a discrete H-1-norm of the exact error. The estimator is further used in the adaptive weak Galerkin algorithm on the triangular, quadrilateral and other polygonal meshes. Numerical results are provided to demonstrate the effectiveness of the adaptive mesh refinement guided by this estimator. (C) 2021 Elsevier B.V. All rights reserved.
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