查看更多>>摘要：We demonstrate the effectiveness of an adaptive explicit Euler method for the approximate solution of the Cox-Ingersoll-Ross model. This relies on a class of path-bounded timestepping strategies which work by reducing the stepsize as solutions approach a neighbourhood of zero. The method is hybrid in the sense that a convergent backstop method is invoked if the timestep becomes too small, or to prevent solutions from overshooting zero and becoming negative. Under parameter constraints that imply Feller's condition, we prove that such a scheme is strongly convergent, of order at least 1/2. Control of the strong error is important for multi-level Monte Carlo techniques. Under Feller's condition we also prove that the probability of ever needing the backstop method to prevent a negative value can be made arbitrarily small. Numerically, we compare this adaptive method to fixed step implicit and explicit schemes, and a novel semi-implicit adaptive variant. We observe that the adaptive approach leads to methods that are competitive in a domain that extends beyond Feller's condition, indicating suitability for the modelling of stochastic volatility in Heston-type asset models. (C) 2022 The Author(s). Published by Elsevier B.V.
查看更多>>摘要：In this paper, we study the low-tubal-rank tensor completion problem, i.e., the problem of recovering a third-order tensor by observing a subset of its entries, when these entries are selected uniformly at random. We propose a mathematical analysis of an extension of the Burer-Monteiro factorisation approach to this problem. We then illustrate the use of the Burer-Monteiro approach on a challenging OCT reconstruction problem on both synthetic and real world data, using an alternating minimisation algorithm.(c) 2022 Published by Elsevier B.V.
查看更多>>摘要：In this paper, we first propose different combination methods to compute the Cauchy principal value integrals of oscillatory Bessel functions. By special transformations, the considered integrals are converted to finite integrals and infinite integrals. Then, the finite integrals can be calculated through the Filon-type method, the Clenshaw-Curtis- Filon method and the Clenshaw-Curtis-Filon-type method, respectively. We compute the infinite integral through the numerical steepest descent method. Moreover, the error analysis with respect to frequency omega is given through theoretical analysis. Eventually, we present several numerical experiments which are in accord with our analysis. Particularly, the accuracy can be improved by either using more nodes or adding more derivatives interpolation at endpoints. The accuracy will increase drastically with the growth of frequency omega if both the number of nodes and interpolated multiplicity are fixed. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：The estimation of the quadrature error of a Gauss quadrature rule when applied to the approximation of an integral determined by a real-valued integrand and a real-valued nonnegative measure with support on the real axis is an important problem in scientific computing. Laurie developed anti-Gauss quadrature rules as an aid to estimate this error. Under suitable conditions the Gauss and associated anti-Gauss rules give upper and lower bounds for the value of the desired integral. It is then natural to use the average of Gauss and anti-Gauss rules as an improved approximation of the integral. Laurie also introduced these averaged rules. More recently, Spalevic derived new averaged Gauss quadrature rules that have higher degree of exactness for the same number of nodes as the averaged rules proposed by Laurie. Numerical experiments reported in this paper show both kinds of averaged rules to often give much higher accuracy than can be expected from their degrees of exactness. This is important when estimating the error in a Gauss rule by an associated averaged rule. We use techniques similar to those employed by Trefethen in his investigation of Clenshaw-Curtis rules to shed light on the performance of the averaged rules. The averaged rules are not guaranteed to be internal, i.e., they may have nodes outside the convex hull of the support of the measure. This paper discusses three approaches to modify averaged rules to make them internal.(c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we investigate the number of failed components in an operating coherent system. We assume that its components are of multiple types. That is, the system consists of components having nonidentical failure time distributions. We extend the results which are well-known in the literature for k-out-of-n systems. We formulate the optimization problem to determine the optimal values of the number of components of each type together with their arrangement in the system. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this work, we propose two new iterative schemes for finding an element of the set of solutions of a pseudo-monotone, Lipschitz continuous variational inequality problem in real Hilbert spaces. The weak and strong convergence theorems are presented. The advantage of the proposed algorithms is that they do not require prior knowledge of the Lipschitz constant of the variational inequality mapping and only compute one projection onto a feasible set per iteration as well as without using the sequentially weakly continuity of the associated mapping. Under additional strong pseudo-monotonicity and Lipschitz continuity assumptions, we obtain also an R-linear convergence rate of the proposed algorithm. Finally, some numerical examples are given to illustrate the effectiveness of the algorithms. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We consider an exterior linear elastodynamics problem with vanishing initial conditions and Dirichlet datum on the scatterer. We convert the Navier Equation, governing the wave behaviour, into two space-time Boundary Integral Equations (BIEs) whose solution is approximated by the energetic Boundary Element Method (BEM). To apply this technique, we have to set the BIEs in a weak form related to the energy of the differential problem solution at the final time instant of analysis. After the space-time discretization of the weak formulation, we have to deal with double space-time integrals, with a weakly singular kernel depending on primary and secondary wave speeds and multiplied by Heaviside functions. The main purpose of this work is the analysis of these peculiar integrals and the study of suitable quadrature schemes for their approximation. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：A Local discontinuous Galerkin (LDG) finite element method on triangular mesh was introduced and analyzed in Castillo et al. (2000) for elliptic problem with suboptimal order of convergence for the flux variable. The purpose of this work is to develop a LDG finite element method on polytopal mesh that achieves optimal convergence rate for both unknowns, potential u and its gradient q. In our new LDG method, u and q are approximated by polynomials of degree k and k - 1 respectively. Optimal order of convergence are obtained for both unknowns. Numerical results in 2d and 3d are presented to confirm the theory.(C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We developed and analyzed the multiblock mortar expanded mixed method for second order parabolic partial differential equations. This is a domain decomposition method in which the computational domain is expressed as the union of non-overlapping subdomains separated by interfaces. An auxiliary variable is introduced on the interface which represents the pressure and serves as Dirichlet boundary condition for local subdomain problems. The interface variable also plays the part of Lagrange multiplier to enforce flux matching condition on the interfaces. We explored the expanded mixed method to discretize each subdomain. We propose the semi-discrete formulation and address the solvability of the discrete problem. The optimal order convergence is provided for the continuous time case. We also investigate the fully discrete formulation and derived corresponding error estimates. The numerical experiments are conducted to demonstrate the theory developed in the paper.(c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：Low-rank matrix recovery is an ill-posed problem increasingly involved and treated vitally in various fields such as statistics, bioinformatics, machine learning and computer vision. Robust Principle Component Analysis (RPCA) is recently presented as a 2-terms convex optimization model to solve this problem. In this paper a new 3-terms convex model arising from RPCA is proposed to recover the low-rank components from polluted or incomplete observation data. This new model possesses three regularization terms to reduce the ill-posedness of the recovery problem. Essential difficulty in algorithm derivation is how to deal with the non-smooth terms. The ALM method is introduced to solve the original 2-terms RPCA model with convergence guarantee. However, for solving the proposed 3-terms model, its convergence is no longer guaranteed. As a different approach based on fixed point theory, we introduce the proximity operator to handle nonsmoothness, and consequently a new algorithm derived from Fixed-Point Proximity Algorithm (FPPA) is proposed with convergence analysis. Numerical experiments on the problems of RPCA and Motion Capture Data Refinement (MCDR) demonstrate the outstripping effectiveness and efficiency of the proposed algorithm. (c) 2022 Elsevier B.V. All rights reserved.
NSTL
Elsevier