Related papers: A sparse spectral method for fractional differenti…
The ability to resolve detail in the object that is being imaged, named by resolution, is the core parameter of an imaging system. Super-resolution is a class of techniques that can enhance the resolution of an imaging system and even…
Spectral and spectral element methods using Galerkin type formulations are efficient for solving linear fractional PDEs (FPDEs) of constant order but are not efficient in solving nonlinear FPDEs and cannot handle FPDEs with variable-order.…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
A new spectral type method for solving the one dimensional quantum-mechanical Lippmann-Schwinger integral equation in configuration space is described. The radial interval is divided into partitions, not necessarily of equal length. Two…
We present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the…
In this paper, we present numerical procedures to compute solutions of partial differential equations posed on fractals. In particular, we consider the strong form of the equation using standard graph Laplacian matrices and also weak forms…
This paper studies sparse super-resolution in arbitrary dimensions. More precisely, it develops a theoretical analysis of support recovery for the so-called BLASSO method, which is an off-the-grid generalisation of l1 regularization (also…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
We discuss a numerical scheme to solve the continuum Kardar-Parisi-Zhang equation in generic spatial dimensions. It is based on a momentum-space discretization of the continuum equation and on a pseudo-spectral approximation of the…
This is the second part in a series of papers on multi-step schemes for solving coupled forward backward stochastic differential equations (FBSDEs). We extend the basic idea in our former paper [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci.…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
In this paper we consider the numerical solution of fractional differential equations. In particular, we study a step-by-step graded mesh procedure based on an expansion of the vector field using orthonormal Jacobi polynomials. Under mild…
The solution of the Lippman-Schwinger (L-S) integral equation is equivalent to the the solution of the Schroedinger equation. A new numerical algorithm for solving the L-S equation is described in simple terms, and its high accuracy is…
Pseudospectral time domain (PSTD) methods are widely used in many branches of acoustics for the numerical solution of the wave equation, including biomedical ultrasound and seismology. The use of the Fourier collocation spectral method in…
In this work we analyze the dimension-independent convergence property of an abstract sparse quadrature scheme for numerical integration of functions of high-dimensional parameters with Gaussian measure. Under certain assumptions of the…
Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a…
A spectral method for solving linear partial differential equations (PDEs) with variable coefficients and general boundary conditions defined on rectangular domains is described, based on separable representations of partial differential…
We construct non-random bounded discrete half-line Schr\" odinger operators which have purely singular continuous spectral measures with fractional Hausdorff dimension (in some interval of energies). To do this we use suitable sparse…
This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the…
A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading…