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Binary convolutional networks have lower computational load and lower memory foot-print compared to their full-precision counterparts. So, they are a feasible alternative for the deployment of computer vision applications on limited…

Computer Vision and Pattern Recognition · Computer Science 2020-07-29 Mete Can Kaya , Alperen İnci , Alptekin Temizel

Two-dimensional Delaunay triangulation is a fundamental aspect of computational geometry. This paper presents a novel algorithm that is specifically designed to ensure the correctness of 2D Delaunay triangulation, namely the Polygonal…

Computational Geometry · Computer Science 2024-01-17 Sora Sawai , Kazuaki Tanaka , Katsuhisa Ozaki , Shin'ichi Oishi

We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their…

Numerical Analysis · Mathematics 2018-10-23 Hermann Mena , Lena-Maria Pfurtscheller , Tony Stillfjord

We propose a high-performance GPU solver for inverse homogenization problems to design high-resolution 3D microstructures. Central to our solver is a favorable combination of data structures and algorithms, making full use of the parallel…

Optimization and Control · Mathematics 2023-05-26 Di Zhang , Xiaoya Zhai , Ligang Liu , Xiao-Ming Fu

We investigate ways in which an algorithm can improve its expected performance by fine-tuning itself automatically with respect to an unknown input distribution D. We assume here that D is of product type. More precisely, suppose that we…

Data Structures and Algorithms · Computer Science 2011-05-30 Nir Ailon , Bernard Chazelle , Kenneth L. Clarkson , Ding Liu , Wolfgang Mulzer , C. Seshadhri

These notes accompany the open-source code published in GitHub which implements a GPU-based line-segment, surface-triangle intersection algorithm in CUDA. It mentions some relevant works and discusses issues specific to this implementation.…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-09-08 Raymond Leung

Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two…

Data Structures and Algorithms · Computer Science 2019-02-21 Daniel Funke , Peter Sanders , Vincent Winkler

The paper considers the problem of implementation on graphics processors of numerical integration routines for higher order finite element approximations. The design of suitable GPU kernels is investigated in the context of general purpose…

Mathematical Software · Computer Science 2014-03-03 Krzysztof Banaś , Przemysław Płaszewski , Paweł Macioł

Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…

Computational Geometry · Computer Science 2023-11-01 Sariel Har-Peled , Elfarouk Harb

In this paper, we analyze the complexity of natural parallelizations of Delaunay refinement methods for mesh generation. The parallelizations employ a simple strategy: at each iteration, they choose a set of ``independent'' points to insert…

Computational Geometry · Computer Science 2007-05-23 Dan A. Spielman , Shang-hua Teng , Alper Ungor

3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior…

Computer Vision and Pattern Recognition · Computer Science 2025-01-28 Lei Lan , Tianjia Shao , Zixuan Lu , Yu Zhang , Chenfanfu Jiang , Yin Yang

In this article, recent works on 2D Constrained Delaunay triangulation(CDT) algorithms have been reported. Since the review of CDT algorithms presented by de Floriani(Issues on Machine Vision, Springer Vienna, pg. 95--104, 1989), different…

Computational Geometry · Computer Science 2017-07-20 Pranav Kant Gaur , S. K. Bose

As recurrent neural networks become larger and deeper, training times for single networks are rising into weeks or even months. As such there is a significant incentive to improve the performance and scalability of these networks. While…

Machine Learning · Computer Science 2016-04-08 Jeremy Appleyard , Tomas Kocisky , Phil Blunsom

Convolutional gridding is a processor-intensive step in interferometric imaging. While it is possible to use graphics processing units (GPUs) to accelerate this operation, existing methods use only a fraction of the available flops. We…

Instrumentation and Methods for Astrophysics · Physics 2016-06-29 Bruce Merry

The Kernel Polynomial Method (KPM) is one of the fast diagonalization methods used for simulations of quantum systems in research fields of condensed matter physics and chemistry. The algorithm has a difficulty to be parallelized on a…

Computational Physics · Physics 2011-05-30 Shixun Zhang , Shinichi Yamagiwa , Masahiko Okumura , Seiji Yunoki

Given a set $P$ of $n$ points in the plane, we show how to compute in $O(n \log n)$ time a subgraph of their Delaunay triangulation that has maximum degree 7 and is a strong planar $t$-spanner of $P$ with $t =(1+ \sqrt{2})^2 *\delta$, where…

Computational Geometry · Computer Science 2010-03-26 Paz Carmi , Lilach Chaitman

We study the accuracy of triangulation in multi-camera systems with respect to the number of cameras. We show that, under certain conditions, the optimal achievable reconstruction error decays quadratically as more cameras are added to the…

Computer Vision and Pattern Recognition · Computer Science 2018-04-30 Adam Scholefield , Alireza Ghasemi , Martin Vetterli

A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function of two variables, the algorithm produces a hierarchy of triangulations and piecewise polynomial approximations…

Numerical Analysis · Mathematics 2015-03-17 Albert Cohen , Nira Dyn , Frédéric Hecht , Jean-Marie Mirebeau

We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…

Numerical Analysis · Mathematics 2022-08-15 Chao Chen , Per-Gunnar Martinsson

The abundance of data has given machine learning considerable momentum in natural sciences and engineering, though modeling of physical processes is often difficult. A particularly tough problem is the efficient representation of geometric…

Machine Learning · Computer Science 2023-04-21 Andreas Mayr , Sebastian Lehner , Arno Mayrhofer , Christoph Kloss , Sepp Hochreiter , Johannes Brandstetter