Results 41 to 50 of about 3,221,012 (201)
On numerical stability of continued fractions
Математичні СтудіїThe paper considers the numerical stability of the backward recurrence algorithm (BR-algorithm) for computing approximants of the continued fraction with complex elements.
V. Hladun +3 more
doaj +1 more source
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
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
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
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
, 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
Varying the Explanatory Span: Scientific Explanation for Computer Simulations [PDF]
, 2017 This article aims to develop a new account of scientific explanation for computer simulations. To this end, two questions are answered: what is the explanatory relation for computer simulations? And what kind of epistemic gain should be expected?
Durán, Juan Manuel
core +1 more source
Gram Decay and Intrinsic Dimensions of Krylov Subspaces
Numerical Linear Algebra with Applications, Volume 33, Issue 3, June 2026.ABSTRACT Krylov subspace methods solve large sparse linear systems Ax=b$$ Ax=b $$ by building a sequence of polynomial approximations to A−1b$$ {A}^{-1}b $$ from successive matrix‐vector products. In finite precision, the number of numerically independent directions that can be extracted from this sequence is bounded by the intrinsic information ...
Stephen J. Thomas
wiley +1 more source
Математичні СтудіїIn this paper, we consider some numerical aspects of branched continued fractions as special families of functions to represent and expand analytical functions of several complex variables, including generalizations of hypergeometric functions.
R. Dmytryshyn +3 more
doaj +1 more source