Related papers: Fast convolution solvers using moment-matching
Constructing effective image priors is critical to solving ill-posed inverse problems in image processing and imaging. Recent works proposed to exploit image non-local similarity for inverse problems by grouping similar patches and…
We introduce a new arbitrarily high-order method for the rapid evaluation of hyperbolic potentials (space-time integrals involving the Green's function for the scalar wave equation). With $M$ points in the spatial discretization and $N_t$…
This paper considers the recovery of a rank $r$ positive semidefinite matrix $X X^T\in\mathbb{R}^{n\times n}$ from $m$ scalar measurements of the form $y_i := a_i^T X X^T a_i$ (i.e., quadratic measurements of $X$). Such problems arise in a…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
We propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The properties of the method are based on the introduction of an…
We present a fast algorithm for evaluating the (non-smooth) solution of the free-space two-dimensional (2D) scalar wave equation with many point sources, each with a high-frequency band-limited time signature. Such an algorithm is key to an…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
Image subtraction in astronomy is a tool for transient object discovery such as asteroids, extra-solar planets and supernovae. To match point spread functions (PSFs) between images of the same field taken at different times a convolution…
We introduce a fast algorithm for Gaussian process regression in low dimensions, applicable to a widely-used family of non-stationary kernels. The non-stationarity of these kernels is induced by arbitrary spatially-varying vertical and…
In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…
We describe an efficient algorithm for computing the matrix vector products that appear in the numerical resolution of boundary integral equations in 2 space dimension. This work is an extension of the so-called Sparse Cardinal Sine…
We propose fast, exact and efficient algorithms for the convolution of two arbitrary functions on the sphere which speed up computations by a factor \order{\sqrt{N}} compared to present methods where $N$ is the number of pixels. No…
In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the…
In this paper, we develop new affine-invariant algorithms for solving composite convex minimization problems with bounded domain. We present a general framework of Contracting-Point methods, which solve at each iteration an auxiliary…
We present a quasi-linearly scaling, first order polynomial finite element method for the solution of the magnetostatic open boundary problem by splitting the magnetic scalar potential. The potential is determined by solving a Dirichlet…
One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory.…
The quasi-2D electrostatic systems, characterized by periodicity in two dimensions with a free third dimension, have garnered significant interest in many fields. We apply the sum-of-Gaussians (SOG) approximation to the Laplace kernel,…
Kernel adaptive filtering (KAF) integrates traditional linear algorithms with kernel methods to generate nonlinear solutions in the input space. The standard approach relies on the representer theorem and the kernel trick to perform…
We give a new framework for proving the existence of low-degree, polynomial approximators for Boolean functions with respect to broad classes of non-product distributions. Our proofs use techniques related to the classical moment problem…