Related papers: A fully discretised filtered polynomial approximat…
There are several numerical methods for computing approximate zeros of a given univariate polynomial. In this paper, we develop a simple and novel method for determining sharp upper bounds on errors in approximate zeros of a given…
We introduce polystar bodies: compact starshaped sets whose gauge or radial functions are expressible by polynomials, enabling tractable computations, such as that of intersection bodies. We prove that polystar bodies are uniformly dense in…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
We provide an irreducibility test in the ring K[[x]][y] whose complexity is quasi-linear with respect to the valuation of the discriminant, assuming the input polynomial F square-free and K a perfect field of characteristic zero or greater…
In this paper we construct a hierarchy of multivariate polynomial approximation kernels via semidefinite programming. We give details on the implementation of the semidefinite programs defining the kernels. Finally, we show how a symmetry…
This paper derives numerical bounds for and implements the splitting circle method for finding roots of a univariate polynomial in the presence of fixed precision.
We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved…
In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the…
Approximation by polynomials on a triangle is studied in the Sobolev space $W_2^r$ that consists of functions whose derivatives of up to $r$-th order have bounded $L^2$ norm. The first part aims at understanding the orthogonal structure in…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…
Sample- and computationally-efficient distribution estimation is a fundamental tenet in statistics and machine learning. We present SURF, an algorithm for approximating distributions by piecewise polynomials. SURF is: simple, replacing…
The problem of the optimal approximation of circular arcs by parametric polynomial curves is considered. The optimality relates to the curvature error. Parametric polynomial curves of low degree are used and a geometric continuity is…
In the last few years, the notion of optimal polynomial approximant has appeared in the mathematics literature in connection with Hilbert spaces of analytic functions of one or more variables. In the 70s, researchers in engineering and…
The bilateral filter is a non-linear filter that uses a range filter along with a spatial filter to perform edge-preserving smoothing of images. A direct computation of the bilateral filter requires $O(S)$ operations per pixel, where $S$ is…
Polynomial approximations to the inverse of the fermion matrix are used to filter the dynamics of the upper energy scales in HMC simulations. The use of a multiple time-scale integration scheme allows the filtered pseudofermions to be…
In this paper a local approximation method on the sphere is presented. As interpolation scheme we consider a partition of unity method, such as the modified spherical Shepard's method, which uses zonal basis functions (ZBFs) plus spherical…
We sketch an application of proximal algorithms to the deformation of de Rham currents into cycles, which is presented as a convex optimization problem. Emphasis is placed on the use of total variation denoising for differential forms,…
We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'16). Our approximation algorithm can be modified to handle…
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…