Related papers: Computing Differential Equations for Integrals Ass…
We consider an algorithm to approximate complex-valued periodic functions $f(e^{i\theta})$ as a matrix element of a product of $SU(2)$-valued functions, which underlies so-called quantum signal processing. We prove that the algorithm runs…
It is known that there are only finitely many mutation-equivalence classes with a given singularity content, and each of these equivalence classes contains only finitely many minimal polygons. We describe an efficient algorithm to classify…
We develop an efficient numerical scheme for the 3D mean-field spherical dynamo equation. The scheme is based on a semi-implicit discretization in time and a spectral method in space based on the divergence-free spherical harmonic…
We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active,…
In this paper, we are concerned with studying the existence of invariant complex manifolds of two-dimensional holomorphic systems. From the geometric singular perturbation theory we know that if a slow-fast system has associated a normally…
This paper presents a pseudo-spectral method for Dynamic Optimization Problems (DOPs) that allows for tight polynomial bounds to be achieved via flexible sub-intervals. The proposed method not only rigorously enforces inequality…
To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…
We present a new continuation algorithm to find all nondegenerate real solutions to a system of polynomial equations. Unlike homotopy methods, it is not based on a deformation of the system; instead, it traces real curves connecting the…
This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and…
We present an algorithm to compute the annihilator of (i.e., the linear differential equations for) the logarithm of a polynomial in the ring of differential operators with polynomial coefficients. The algorithm consists of differentiation…
Automatic differentiation, as implemented today, does not have a simple mathematical model adapted to the needs of modern machine learning. In this work we articulate the relationships between differentiation of programs as implemented in…
We present a general algorithm for solving all two-variable polynomial Diophantine equations consisting of three monomials. Before this work, even the existence of an algorithm for solving the one-parameter family of equations…
We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a smooth convolution on the unit sphere, a model reduction step…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
Here we present a new approach to compute symmetries of rational second order ordinary differential equations (rational 2ODEs). This method can compute Lie symmetries (point symmetries, dynamical symmetries and non-local symmetries)…
In this paper we analyse the pathwise approximation of stochastic differential equations by polynomial splines with free knots. The pathwise distance between the solution and its approximation is measured globally on the unit interval in…
This paper considers the approximation of partial differential equations with a point collocation framework based on high-order local maximum-entropy schemes (HOLMES). In this approach, smooth basis functions are computed through an…
We study a hypergeometric function in two variables and a system of hypergeometric differential equations associated with this function. This is a regular holonomic system of rank $9$. We give a fundamental system of solutions to this…
We consider the connected-sum method of constructing compact Riemannian 7-manifolds with holonomy G_2 developed in math.DG/0012189. The method requires pairs of projective complex threefolds endowed with anticanonical K3 divisors, the…
This paper is to investigate if the solution of a hybrid stochastic functional differential equation (SFDE) with infinite delay can be approximated by the solution of the corresponding hybrid SFDE with finite delay. A positive result is…