Related papers: Reduction-Based Creative Telescoping for Fuchsian …
In this paper, we build on the work of [T. Hughes, G. Sangalli, VARIATIONAL MULTISCALE ANALYSIS: THE FINE-SCALE GREENS' FUNCTION, PROJECTION, OPTIMIZATION, LOCALIZATION, AND STABILIZED METHODS, SIAM Journal of Numerical Analysis, 45(2),…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
Multi-dimensional distributions of discrete data that resemble ellipsoids arise in numerous areas of science, statistics, and computational geometry. We describe a complete algebraic algorithm to determine the quadratic form specifying the…
Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on…
We study integration in a class of Hilbert spaces of analytic functions defined on the $\mathbb{R}^s$. The functions are characterized by the property that their Hermite coefficients decay exponentially fast. We use Gauss-Hermite…
We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…
We study the asymptotic shape of the trajectory of the stochastic gradient descent algorithm applied to a convex objective function. Under mild regularity assumptions, we prove a functional central limit theorem for the properly rescaled…
In recent years, the use of sparse recovery techniques in the approximation of high-dimensional functions has garnered increasing interest. In this work we present a survey of recent progress in this emerging topic. Our main focus is on the…
In this paper, a new and efficient numerical algorithm by using weak Galerkin (WG) finite element methods is proposed for a type of fourth order problem arising from fluorescence tomography(FT). Fluorescence tomography is an emerging, in…
We identity the optimal non-infinitesimal direction of descent for a convex function. An algorithm is developed that can theoretically minimize a subset of (non-convex) functions.
We derive a novel computational scheme for functional Renormalization Group (fRG) calculations for interacting fermions on 2D lattices. The scheme is based on the exchange parametrization fRG for the two-fermion interaction, with additional…
We present a criterion for the existence of telescopers for mixed hypergeometric terms, which is based on multiplicative and additive decompositions. The criterion enables us to determine the termination of Zeilberger's algorithms for mixed…
We propose a differential analog of the notion of integral closure of algebraic function fields. We present an algorithm for computing the integral closure of the algebra defined by a linear differential operator. Our algorithm is a direct…
This paper presents an algorithmic framework for the minimization of strictly convex quadratic functions. The framework is flexible and generic. At every iteration the search direction is a linear combination of the negative gradient, as…
From the algebraic solution of $x^{n}-x+t=0$ for $n=2,3,4$ and the corresponding solution in terms of hypergeometric functions, we obtain a set of reduction formulas for hypergeometric functions. By differentiation and integration of these…
This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…
We consider the numerical evaluation of the quantity $Af(A^{-1}B)$, where $A$ is Hermitian positive definite, $B$ is Hermitian, and $f$ is a function defined on the spectrum of $A^{-1}B$. This problem is related to the Hermitian-definite…
The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains, are strongly affected by the amplitude of the Gaussian weight function employed to describe…
We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint interpolation of points and associated tangents on a curve…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…