Concept
Horner's method
Related publications (18)
Linear Complexity Self-Attention With 3rd Order Polynomials
Grigorios Chrysos, Filippos Kokkinos
Self-attention mechanisms and non-local blocks have become crucial building blocks for state-of-the-art neural architectures thanks to their unparalleled ability in capturing long-range dependencies in the input. However their cost is quadratic with the nu ...
Los Alamitos2023Quadrature-free immersed isogeometric analysis
Pablo Antolin Sanchez, Thibaut Hirschler
This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a newly developed technique for the eva ...
SPRINGER2022MATHICSE Technical Report: THU-Splines - Highly Localized Refinement on Smooth Unstructured Splines
We present a novel method named truncated hierarchical unstructured splines (THU-splines) that supports both local h-refinement and unstructured quadrilateral meshes. In a THU-spline construction, an unstructured quadrilateral mesh is taken as the input co ...
MATHICSE2021Support and approximation properties of Hermite splines
Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Shayan Aziznejad
In this paper, we formally investigate two mathematical aspects of Hermite splines that are relevant to practical applications. We first demonstrate that Hermite splines are maximally localized, in the sense that the size of their support is minimal among ...
2020Momentum space CFT correlators for Hamiltonian truncation
We consider Lorentzian CFT Wightman functions in momentum space. In particular, we derive a set of reference formulas for computing two- and three-point functions, restricting our attention to three-point functions where the middle operator (corresponding ...
2020An Improved Analysis of Local Search for Max-Sum Diversification
Friedrich Eisenbrand, Rico Zenklusen, Alfonso Bolívar Cevallos Manzano
We present new techniques to analyze natural local search algorithms for several variants of the max-sum diversification problem which, in its most basic form, is as follows: given an n-point set X subset of R-d and an integer k, select k points in X so th ...
INFORMS2019Combinatorial Algorithm for Restricted Max-Min Fair Allocation
Ola Nils Anders Svensson, Christos Kalaitzis, Chidambaram Annamalai
We study the basic allocation problem of assigning resources to players to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, a certain ...
Association for Computing Machinery2017Approximation algorithms for geometric dispersion
Alfonso Bolívar Cevallos Manzano
The most basic form of the max-sum dispersion problem (MSD) is as follows: given n points in R^q and an integer k, select a set of k points such that the sum of the pairwise distances within the set is maximal. This is a prominent diversity problem, with w ...
EPFL2016Combinatorial Algorithm for Restricted Max-Min Fair Allocation
Ola Nils Anders Svensson, Christos Kalaitzis, Chidambaram Annamalai
We study the basic allocation problem of assigning resources to players so as to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, a ce ...
2014On the evaluation of hyper-singular double normal derivative kernels in surface integral equation methods
A stable and efficient numerical scheme for the evaluation of surface integrals with 1/R-3-type singularities is presented. The method is based on the combination of the direct evaluation method and the singularity subtraction technique. The proposed metho ...
Elsevier2013