Concept

Machine epsilon

Related publications (23)

On the Sums over Inverse Powers of Zeros of the Hurwitz Zeta Function and Some Related Properties of These Zeros

Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of the analytical function to find the sums over inverse powers of zeros for the incomplete gamma and Riemann zeta functions, polygamma functions, an ...

MDPI2024

Impact of Redundancy on Resilience in Distributed Optimization and Learning

Nirupam Gupta, Shuo Liu

This paper considers the problem of resilient distributed optimization and stochastic learning in a server-based architecture. The system comprises a server and multiple agents, where each agent has its own local cost function. The agents collaborate with ...

Assoc Computing Machinery2023

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Daniel Kressner, Ivana Sain Glibic

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

SPRINGER2023

CosmoLattice: A modern code for lattice simulations of scalar and gauge field dynamics in an expanding universe

Daniel Garcia Figueroa, Adrien Florio, Wessel Valkenburg

This paper describes CosmoGattice, a modern package for lattice simulations of the dynamics of interacting scalar and gauge fields in an expanding universe. CosmoGattice incorporates a series of features that makes it very versatile and powerful: i) it is ...

ELSEVIER2023

TimeEvolver: A program for time evolution with improved error bound

Sebastian Zell

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

ELSEVIER2022

How important are the residual nonadiabatic couplings for an accurate simulation of nonadiabatic quantum dynamics in a quasidiabatic representation?

Jiri Vanicek, Seonghoon Choi

Diabatization of the molecular Hamiltonian is a standard approach to remove the singularities of nonadiabatic couplings at conical intersections of adiabatic potential energy surfaces. In general, it is impossible to eliminate the nonadiabatic couplings en ...

2021

ColTraIn: Co-located DNN training and inference

Mario Paulo Drumond Lages De Oliveira

Deep neural network inference accelerators are deployed at scale to accommodate online services, but face low average load because of service demand variability, leading to poor resource utilization. Unfortunately, reclaiming inference idle cycles is diffi ...

EPFL2020

Differentially Private Release of Synthetic Graphs

Mikhail Kapralov, Marek Elias

We propose a (epsilon, delta)-differentially private mechanism that, given an input graph G with n vertices and m edges, in polynomial time generates a synthetic graph G' approximating all cuts of the input graph up to an additive error of O (root mn/epsil ...

ASSOC COMPUTING MACHINERY2020

Global Flux-Driven Simulations of Ion Temperature-Gradient and Trapped-Electron Modes Driven Turbulence with an Improved Multithreaded Gyrokinetic PIC Code

Emmanuel Lanti

Performance of tokamak fusion plasmas is heavily linked to the radial heat and particle transport, which is known to be mainly produced by turbulence driven by micro-instabilities. Understanding such processes is thus of key importance for the design and o ...

EPFL2019

PyLandStats: An open-source Pythonic library to compute landscape metrics

Martí Bosch Padrós

Quantifying the spatial pattern of landscapes has become a common task of many studies in landscape ecology. Most of the existing software to compute landscape metrics is not well suited to be used in interactive environments such as Jupyter notebooks nor ...

2019

Improved Massively Parallel Computation Algorithms for MIS, Matching, and Vertex Cover

Slobodan Mitrovic

We present O(log log n)-round algorithms in the Massively Parallel Computation (MPC) model, with a(n) memory per machine, that compute a maximal independent set, a 1 + epsilon approximation of maximum matching, and a 2 + epsilon approximation of minimum ve ...

ASSOC COMPUTING MACHINERY2018

Towards a Compiler for Reals

Viktor Kuncak, Eva Darulova

Numerical software, common in scientific computing or embedded systems, inevitably uses a finite-precision approximation of the real arithmetic in which most algorithms are designed. In many applications, the roundoff errors introduced by finite-precision ...

2017

Renormalization and blow up for wave maps from $S^2 \times \mathbb{R}$ to $S^2$

Sohrab Mirshams Shahshahani

We construct a one parameter family of nite time blow ups to the co-rotational wave maps problem from

S^2\times R

S^2

parameterized by

\nu \epsilon (\frac{1}{2},1]

. The longitudinal function

u(t,\alpha)

which is the main object of study will be ...

2016

Approximate BDD Optimization with Prioritized epsilon-Preferred Evolutionary Algorithm

Mathias Soeken

Approximate computing has gained high attention in various applications that can benefit from a reduction in costs by lowering the accuracy. In this paper we present an optimization approach for functional approximation of Binary Decision Diagrams (BDDs) w ...

Assoc Computing Machinery2016

Automatic Generation of Inexact Digital Circuits by Gate-level Pruning

Christian Enz, Vincent Frédéric Camus, Jérémy Lucien Maurice Schlachter

Inexact or approximate circuits show great ability to reduce power consumption at the cost of occasional errors in comparison to their conventional counterparts. Even though the benefits of such circuits have been proven for many applications, they are not ...

2015

Homogenization of a multiscale viscoelastic model with nonlocal damping, application to the human lungs

Paul Isaac Denis Louis Marie Cazeaux

We are interested in the mathematical modeling of the deformation of the human lung tissue, called the lung parenchyma, during the respiration process. The parenchyma is a foam-like elastic material containing millions of air-filled alveoli connected by a ...

World Scientific Publ Co Pte Ltd2015

Aggressively Truncated Taylor Series Method For Accurate Computation Of Exponentials Of Essentially Nonnegative Matrices

Meiyue Shao

Small relative perturbations to the entries of an essentially nonnegative matrix introduce small relative errors to entries of its exponential. It is thus desirable to compute the exponential with high componentwise relative accuracy. Taylor series approxi ...

Siam Publications2014

Programming with Numerical Uncertainties

Eva Darulova

Numerical software, common in scientific computing or embedded systems, inevitably uses an approximation of the real arithmetic in which most algorithms are designed. In many domains, roundoff errors are not the only source of inaccuracy and measurement as ...

EPFL2014

Fast Directional Spatially Localized Spherical Harmonic Transform

Yves Wiaux, Jason Douglas McEwen

We propose a transform for signals defined on the sphere that reveals their localized directional content in the spatio-spectral domain when used in conjunction with an asymmetric window function. We call this transform the directional spatially localized ...

Institute of Electrical and Electronics Engineers2013

Randomized recovery for boolean compressed sensing

Martin Vetterli, Mitra Fatemi

We consider the problem of boolean compressed sensing, which is alternatively known as group testing. The goal is to recover a small number of defective items in a large set from a few collective binary tests. This problem can be formulated as a binary lin ...

2013