Results 221 to 230 of about 84,372 (264)

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
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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
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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
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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 ...
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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
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Reduce Rounding Off Errors in Information Dispersal Algorithm

2019 International Conference on Computer, Control, Informatics and its Applications (IC3INA), 2019
The Information Dispersal Algorithm (IDA) is an algorithm that can be used to store files securely. Files and data packets can be broken down at the bit level into several parts and then saved to separate nodes. IDA requires a matrix generator in the form of the Vandermonde matrix and the Cauchy matrix to split and reconstruct files.
Ardhi Wijayanto, Bambang Harjito
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Round-off errors andp-adic numbers

Nonlinearity, 1999
Summary: We explore some connections between round-off errors in linear planar rotations and algebraic number theory. We discretize a map on a lattice in such a way as to retain invertibility, restricting the system parameter (the trace) to rational values with power-prime denominator \(p^n\).
Bosio, D., Vivaldi, F.
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CADNA: a library for estimating round-off error propagation

Computer Physics Communications, 2008
The CADNA library enables one to estimate round-off error propagation using a probabilistic approach. With CADNA the numerical quality of any simulation program can be controlled. Furthermore by detecting all the instabilities which may occur at run time, a numerical debugging of the user code can be performed.
Jézéquel, Fabienne, Chesneaux, Jean-Marie   +1 more
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Automatic propagated and round-off error analysis

Preprints of papers presented at the 13th national meeting of the Association for Computing Machinery on - ACM '58, 1958
The routine described below is a modification of the Carnegie Tech (IT) Compiler system for the IBM-650, which will provide automatic empirical analysis of propagated and round-off errors in computation. In the modified system, three kinds of variables are admissable: fixed-point integers called I-variables; floating-point numbers called C-variables ...
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Round-off errors in variational calculations

Journal of Computational Physics, 1968
Abstract Rigorous bounds are derived for the effect of round-off errors in variational calculations for eigenvalues of linear operators. These bounds are simple to compute. They are used to derive an alternative variation principle which minimizes the effect of round-off errors. A numerical example of the use of the techniques is given.
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