相关论文: A new variational principle for the Euclidean dist…

We propose a novel variational method to compute a highly accurate global signed distance function (SDF) to a given point cloud. To this end, the jump set of the gradient of the SDF, which coincides with the medial axis of the surface, is…

We establish rigorously convergence of a semi-discrete upwind scheme for the nonlinear variational wave equation $u_{tt} - c(u)(c(u) u_x)_x = 0$ with $u|_{t=0}=u_0$ and $u_t|_{t=0}=v_0$. Introducing Riemann invariants $R=u_t+c u_x$ and…

In the present article we study strong approximation of solutions of scalar stochastic differential equations (SDEs) with bounded and $\alpha$-H\"older continuous drift coefficient and constant diffusion coefficient at time point $1$.…

This paper deals with the backward Euler method applied to semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive noise. The SPDE is discretized in space by the finite element method and in time by the…

We developed fast direct solver for 3D Helmholtz and Maxwell equations in layered medium. The algorithm is based on the ideas of cyclic reduction for separable matrices. For the grids with major uniform part (within the survey domain in the…

This paper presents a linear computational technique based on cubic trigonometric cubic B-splines for time fractional burgers' equation. The nonlinear advection term is approximated by a new linearization technique which is very efficient…

Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially…

In this paper, we approximate numerically the solution of Caputo-type advection-diffusion equations of the form $D_t^{\alpha} u(t,x) = a_1(x)u_{xx}(t,x) + a_2(x)u_x(t,x) + a_3u(t,x) + a_4(t,x)$, where $D_t^{\alpha} u$ denotes the Caputo…

In this paper we develop a new approach to the design of direct numerical methods for multidimensional problems of the calculus of variations. The approach is based on a transformation of the problem with the use of a new class of…

Value functions arise as a component of algorithms as well as performance metrics in statistics and engineering applications. Computation of the associated Bellman equations is numerically challenging in all but a few special cases. A…

The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic…

Traditional methods for solving physical equations in curved spaces, especially in fluid mechanics and general relativity, rely heavily on the use of Christoffel symbols. These symbols provide the necessary corrections to account for…

Pairwise Euclidean distance calculation is a fundamental step in many machine learning and data analysis algorithms. In real-world applications, however, these distances are frequently distorted by heteroskedastic noise$\unicode{x2014}$a…

This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…

In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To start with, an implicit difference method based on two-sided…

The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the…

Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the…

We propose a new unsupervised anomaly detection method based on the sliced-Wasserstein distance for training data selection in machine learning approaches. Our filtering technique is interesting for decision-making pipelines deploying…

This study debuts a new spline dimensional decomposition (SDD) for uncertainty quantification analysis of high-dimensional functions, including those endowed with high nonlinearity and nonsmoothness, if they exist, in a proficient manner.…

Since it is difficult to implement implicit schemes on the infinite-dimensional space, we aim to develop the explicit numerical method for approximating super-linear stochastic functional differential equations (SFDEs). Precisely, borrowing…