Results 1 to 10 of about 3,259,600 (159)

On the distributions of significant digits and roundoff errors

Communications of the ACM, 1974
Generalized logarithmic law is derived for the distribution of the first t significant digits of a random digital integer. This result is then used to determine the distribution of the roundoff errors in floating-point operations, which is a mixture of uniform and reciprocal distributions.
N. Tsao
exaly   +3 more sources

Tests of probabilistic models for propagation of roundoff errors

Communications of the ACM, 1966
In any prolonged computation it is generally assumed that the accumulated effect of roundoff errors is in some sense statistical. The purpose of this paper is to give precise descriptions of certain probabilistic models for roundoff error, and then to describe a series of experiments for testing the validity of these models.
T E Hull
exaly   +4 more sources

Cycles and circles in roundoff errors. [PDF]

Physical Review E, 1993
When a series of measurements is performed with increasingly coarse (or increasingly fine) precision, consecutive observations seem to be erratically distributed at first, and then organize themselves into cycles and patterns.
Szpiro
semanticscholar   +4 more sources

Degeneracy in the presence of roundoff errors

Linear Algebra and its Applications, 1988
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R. Fletcher
semanticscholar   +2 more sources

On Local Roundoff Errors in Floating-Point Arithmetic

Journal of the ACM, 1973
A bound on the relative error in floating-point addition using a single-precision accumulator with guard digits is derived. It is shown that even with a single guard digit, the accuracy can be almost as good as that using a double-precision accumulator.
T. Kaneko, Bede Liu
semanticscholar   +3 more sources

Efficient Calculation of the Effects of Roundoff Errors

ACM Transactions on Mathematical Software, 1978
J. Larson, A. Sameh
semanticscholar   +3 more sources

On the calculation of the effects of roundoff errors

ACM Transactions on Mathematical Software, 1981
E. Ukkonen
semanticscholar   +3 more sources

FAST ROBUST ARITHMETICS FOR GEOMETRIC ALGORITHMS AND APPLICATIONS TO GIS [PDF]

The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2021
Geometric predicates are used in many GIS algorithms, such as the construction of Delaunay Triangulations for Triangulated Irregular Networks (TIN) or geospatial predicates.
T. Bartels, V. Fisikopoulos
doaj   +1 more source

Accounting for Round-Off Errors When Using Gradient Minimization Methods

Algorithms, 2022
This paper discusses a method for taking into account rounding errors when constructing a stopping criterion for the iterative process in gradient minimization methods.
Dmitry Lukyanenko, Valentin Shinkarev, Anatoly Yagola   +2 more
doaj   +1 more source

Parallel Algorithm for Solving Overdetermined Systems of Linear Equations, Taking into Account Round-Off Errors

Algorithms, 2023
The paper proposes a parallel algorithm for solving large overdetermined systems of linear algebraic equations with a dense matrix. This algorithm is based on the use of a modification of the conjugate gradient method, which is able to take into account ...
Dmitry Lukyanenko
doaj   +1 more source