Results 31 to 40 of about 7,065 (184)
A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4
, 2018 Being able to soundly estimate roundoff errors of finite-precision computations is important for many applications in embedded systems and scientific computing.
Becker, Heiko +5 more
core +1 more source
, 1998 Numerical integrations in celestial mechanics often involve the repeated computation of a rotation with a constant angle. A direct evaluation of these rotations yields a linear drift of the distance to the origin.
Danby +11 more
core +3 more sources
On Sound Relative Error Bounds for Floating-Point Arithmetic
, 2017 State-of-the-art static analysis tools for verifying finite-precision code compute worst-case absolute error bounds on numerical errors. These are, however, often not a good estimate of accuracy as they do not take into account the magnitude of the ...
baranowski +9 more
core +1 more source
Testing the Accuracy and Stability of Spectral Methods in Numerical Relativity [PDF]
, 2007 The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the KST representation of the Einstein evolution equations. The basic "Mexico City Tests" widely adopted by the numerical relativity community are adapted here for ...
Harald P. Pfeiffer +6 more
core +2 more sources
Register‐Efficient Linear‐Time Evaluation in the Bernstein Basis
Computer Graphics Forum, EarlyView.Abstract We investigate the evaluation of points and derivatives of Bézier curves and surfaces on modern architectures, focusing on performance and guided by numerical error bounds. While the de Casteljau algorithm remains the reference for numerical robustness, its linear working‐set size imposes substantial register pressure on GPUs.
Gábor Valasek, Anna Lili Horváth
wiley +1 more source
Quantization in Control Systems and Forward Error Analysis of Iterative Numerical Algorithms [PDF]
, 2010 The use of control theory to study iterative algorithms, which can be considered as dynamical systems, opens many opportunities to find new tools for analysis of algorithms.
Constantinides, GA +2 more
core +2 more sources
A stochastic roundoff error analysis for the convolution [PDF]
Mathematics of Computation, 1992 We study the accuracy of an algorithm which computes the convolution via Radix-2 fast Fourier transforms. Upper bounds are derived for the expected value and the variance of the accompanying linear forms in terms of the expected value and variance of the relative roundoff errors for the elementary operations of addition and multiplication.
openaire +1 more source
The Role of Dice in the Emergence of the Probability Calculus
International Statistical Review, EarlyView.Summary The early development of the probability calculus was clearly influenced by the roll of dice. However, while dice have been cast since time immemorial, documented calculations on the frequency of various dice throws date back only to the mid‐13th century.
David R. Bellhouse, Christian Genest
wiley +1 more source
Roundoff errors in the problem of computing Cauchy principal value integrals
, 2015 We investigate the possibility of fast, accurate and reliable computation of the Cauchy principal value integrals $\mathrm{P}\!\int_{a}^{b} f(x)(x-\tau)^{-1} dx$ $(a < \tau < b)$ using standard adaptive quadratures. In order to properly control the error
Keller, Paweł, Wróbel, Iwona
core +1 more source
Self-similar Singularity of a 1D Model for the 3D Axisymmetric Euler Equations [PDF]
, 2015 We investigate the self-similar singularity of a 1D model for the 3D axisymmetric Euler equations, which is motivated by a particular singularity formation scenario observed in numerical computation.
Hou, Thomas Y., Liu, Pengfei
core +5 more sources