Results 241 to 250 of about 179,143 (282)

Round-off error in products

Computing, 1975
LetA 1 andA 2 be floating point numbers represented in arbitrary base β and randomly chosen from a logarithmic distribution. Letr denote the round-off error $$r = fl(A_1 * A_2 ) - (A_1 * A_2 )$$ where * is floating point multiplication and wherefl(A 1*A 2 ...
Richard Goodman, Alan Feldstein
openaire   +1 more source

Mean and variance of round off error

Signal Processing, 2016
Gadzhiev [4] derived expressions for round off error mean and round off error variance when the rounded variable follows the centered uniform and centered Gaussian distributions. Here, we derive general expressions for round off error mean and round off error variance when the rounded variable is any continuous random variable on the real line or any ...
Rui Li, Saralees Nadarajah
openaire   +2 more sources

Automatic Estimation of Verified Floating-Point Round-Off Errors via Static Analysis

International Conference on Computer Safety, Reliability, and Security, 2017
This paper introduces a static analysis technique for computing formally verified round-off error bounds of floating-point functional expressions. The technique is based on a denotational semantics that computes a symbolic estimation of floating-point ...
Mariano M. Moscato, Laura Titolo, Aaron Dutle, C. Muñoz   +3 more
semanticscholar   +1 more source

On the hypothesis of the independence of round-off errors in numerical integration

USSR Computational Mathematics and Mathematical Physics, 1964
N. Bakhvalov
exaly   +2 more sources

ROUND-OFF ERRORS IN IMPLICIT FINITE DIFFERENCE METHODS

The Quarterly Journal of Mechanics and Applied Mathematics, 1956
A. R. Mitchell
semanticscholar   +3 more sources

Complexity Estimates Depending on Condition and Round-off Error

Journal of the ACM, 1998
This paper has two agendas. One is to develop the foundations of round-off in computation. The other is to describe an algorithm for deciding feasibility for polynomial systems of equations and inequalities together with its complexity analysis and its round-off properties. Each role reinforces the other.
Felipe Cucker, Steve Smale
openaire   +1 more source

ROUNDING-OFF ERRORS IN MATRIX PROCESSES

The Quarterly Journal of Mechanics and Applied Mathematics, 1948
A number of methods of solving sets of linear equations and inverting matrices are discussed. The theory of the rounding-off errors involved is investigated for some of the methods. In all cases examined, including the well-known 'Gauss elimination process', it is found that the errors are normally quite moderate: no exponential build-up need occur ...
openaire   +2 more sources

Accumulation of Round-Off Error in Fast Fourier Transforms

Journal of the ACM, 1970
The fast Fourier transform (FFT) is an algorithm to compute the discrete Fourier coefficients with a substantial time saving over conventional methods. The finite word length used in the computer causes an error in computing the Fourier coefficients.
Toyohisa Kaneko, Bede Liu
openaire   +2 more sources

A Round-Off Error Model with Applications to Arithmetic Expressions

SIAM Journal on Computing, 1979
An arithmetic expression is evaluated in a form most suitable to a given computing structure. To select this “suitable form” restructuring algorithms using laws of associativity, commutativity, and distributivity have been proposed. This raises the question of how different ways of evaluating an expression influence the propagation of errors due to ...
Vijay B. Aggarwal, James W. Burgmeier
openaire   +2 more sources

Round-Off Error Analysis in mMIMO Detector Based on Cholesky Decomposition

IEEE Wireless Communications Letters
In this letter, we propose a new approach to justify a round-off error impact on the performance of a low-precision Massive Multiple Input, Multiple Output (MIMO) detector based on Cholesky decomposition.
Alexander Osinsky, Roman Bychkov, M. Trefilov, V. Lyashev, A. Ivanov   +4 more
semanticscholar   +1 more source