相关论文: Fast two-scale methods for Eikonal equations

Detecting spatial patterns is fundamental to scientific discovery, yet current methods lack statistical consensus and face computational barriers when applied to large-scale spatial omics datasets. We unify major approaches through a single…

Approximate message-passing (AMP) method is a simple and efficient framework for the linear inverse problems. In this letter, we propose a faster AMP to solve the \emph{$L_1$-Split-Analysis} for the 2D sparsity separation, which is referred…

Recently, the mapping approach to surface hopping (MASH) was proposed as a method to simulate the non-adiabatic dynamics of two-level systems. It was shown that the method possesses many desirable qualities, both theoretically and through…

We propose a novel multiple-scale spatial marching method for flows with slow streamwise variation. The key idea is to couple the boundary region equations, which govern large-scale flow evolution, with local exact coherent structures that…

We present algorithms for solving high-frequency acoustic scattering problems in complex domains. The eikonal and transport partial differential equations from the WKB/geometric optic approximation of the Helmholtz equation are solved…

There has been a large increase in the amount of work on hierarchical low-rank approximation methods, where the interest is shared by multiple communities that previously did not intersect. This objective of this article is two-fold; to…

In this paper, the steady creeping flow equations of a second grade fluid in cartesian coordinates are considered; the equations involve a small parameter related to the dimensionless non--Newtonian coefficient. According to a recently…

This paper focuses on utilizing two different Bayesian methods to deal with a variety of toy problems which occur in data analysis. In particular we implement the Variational Bayesian and Nested Sampling methods to tackle the problems of…

Recent developments in the theory and application of the Hardy-Littlewood method are discussed, concentrating on aspects associated with diagonal diophantine problems. Recent efficient differencing methods for estimating mean values of…

A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of…

Fixed-point iterative sweeping methods were developed in the literature to efficiently solve steady state solutions of Hamilton-Jacobi equations and hyperbolic conservation laws. Similar as other fast sweeping schemes, the key components of…

In this paper, we develop fast procedures for solving linear systems arising from discretization of ordinary and partial differential equations with Caputo fractional derivative w.r.t time variable. First, we consider a finite difference…

We present two (a decoupled and a coupled) integral-equation-based methods for the Morse-Ingard equations subject to Neumann boundary conditions on the exterior domain. Both methods are based on second-kind integral equation (SKIE)…

We propose a Fast Marching based implementation for computing sub-Riemanninan (SR) geodesics in the roto-translation group SE(2), with a metric depending on a cost induced by the image data. The key ingredient is a Riemannian approximation…

We propose a fast integrator to a class of dynamical systems with several temporal scales. The proposed method is developed as an extension of the variable step size Heterogeneous Multiscale Method (VSHMM), which is a two-scale integrator…

The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that…

The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…

The problem of approximating a sampled function using sums of a fixed number of complex exponentials is considered. We use alternating projections between fixed rank matrices and Hankel matrices to obtain such an approximation. Convergence,…

We consider sweeping domain decomposition preconditioners to solve the Helmholtz equation in the case of stripwise domain decomposition with or without overlaps. We unify their derivation and convergence studies by expressing them as…

Detecting maximal square submatrices of ones in binary matrices is a fundamental problem with applications in computer vision and pattern recognition. While the standard dynamic programming (DP) solution achieves optimal asymptotic…