Results 101 to 110 of about 337 (147)

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.
Thomas E. Hull, J. Richard Swenson
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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.
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Symplectic Integrators: Rotations and Roundoff Errors

Celestial Mechanics and Dynamical Astronomy, 1998
We investigate the numerical implementation of a symplectic integrator combined with a rotation (as in the case of an elongated rotating primary). We show that a straightforward implementation of the rotation as a matrix multiplication destroys the conservative property of the global integrator, due to roundoff errors.
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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.
Toyohisa Kaneko, Bede Liu
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Roundoff Errors in Signal Averaging Systems

IEEE Transactions on Biomedical Engineering, 1986
In biomedical signal averaging applications where a small repetitive signal is to be extracted form a very noisy waveform (noise variance ?2n), the A/D converter range is set at ±A?n where A typically has a value of 3 or 4. In this case, A/D roundoff noise using a (b + 1)-bit A/D converter degrades the SNR of the resulting signal estimate by an amount ...
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Numerical chaos, roundoff errors, and homoclinic manifolds

Physical Review Letters, 1993
The focusing nonlinear Schr\"odinger equation is numerically integrated over moderate to long time intervals. In certain parameter regimes small errors on the order of roundoff grow rapidly and saturate at values comparable to the main wave. Although the constants of motion are nearly preserved, a serious phase instability (chaos) develops in the ...
, Ablowitz, , Schober, , Herbst
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Roundoff errors for polynomial evaluation by a family of formulae

Computing, 2008
The classical Lagrange interpolation formula is rewritten in the barycentric form. The authors show that these kind of formulas can be analyzed by making a distinction between the first steps corresponding to computations to high relative accuracy and the final sum, where high relative accuracy cannot be ensured.
Jesús M. Carnicer, Tim N. T. Goodman, Juan Manuel Peña 0001   +2 more
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Roundoff errors in block-floating-point systems

IEEE Transactions on Signal Processing, 1996
Block-floating-point representation is a special case of floating-point representation, where several numbers have a joint exponent term. In this paper, roundoff errors in signal processing systems utilizing block-floating-point representation are studied. Special emphasis is on analysis of quantization errors when data is quantized to a block-floating-
Kari Kalliojärvi, Jaakko Astola
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A roundoff error analysis of the Oja's subspace rule

1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2002
This paper deals with the effects of finite precision data representation and arithmetic in principal component analysis (PCA) networks. PCA or Karhunen Loeve transform (KLT) is a statistical method that determines an optimal linear transformation of input vectors of a stationary stochastic process.
Tamás Szabó, Gábor Horváth 0001
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Avoiding Roundoff Error in Backpropagating Derivatives

1998
One significant source of roundoff error in backpropagation networks is the calculation of derivatives of unit outputs with respect to their total inputs. The roundoff error can lead result in high relative error in derivatives, and in particular, derivatives being calculated to be zero when in fact they are small but non-zero.
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