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On the statistics of fixed-point roundoff error
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1985Roundoff error after fixed-point multiplication is commonly modeled as uniformly distributed white noise that is uncorrelated with the signal. This paper presents a statistical analysis of fixed-point roundoff error that identifies the conditions under which this model is valid, and examines the statistical behavior of roundoff error when these ...
Casper W. Barnes +2 more
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A new iterative refinement with roundoff error analysis
Numerical Linear Algebra With Applications, 2011AbstractIn this paper we present a novel improvement of Wilkinson's iterative refinement for the solution of linear system by using stability results of numerical solution for a dynamic system associated with the linear system. The convergence analysis is shown and roundoff error analysis is considered for this new refinement. Numerical experiments are
Zhengyu Wang
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On the variance of a centered random value roundoff error
Signal Processing, 2015We derive two expressions for roundoff error variance, one for a rounded off random value with a zero mean and a given variance under uniform distribution and another for such a value under a normal. Also, an expression for truncation error variance for values under uniform distribution is obtained.
Y. A. Gadzhiev
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Impact of roundoff errors in LDPC decoding
2008 3rd International Symposium on Wireless Pervasive Computing, 2008In this paper the impact of roundoff mechanisms on the performance of message-passing LDPC decoding is studied. It is shown that finite word length introduces error by means of two mechanisms, each of which is analyzed. The impact and behavior of the two mechanisms are clarified by experimental results.
Nikos Kanistras, Vassilis Paliouras
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Algorithms for roundoff error analysis —A relative error approach
Computing, 1980Methods are presented for performing various error analyses of numerical algorithms. These analyses include forward, backward, and B-analysis (a combination of forward and backward). These analyses additionally provide alternative criteria by which different algorithms that solve the same problem may be compared.
John L. Larson, Ahmed H. Sameh
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Quantization and Roundoff Errors
1989A one-dimensional (1-D) digital filter, as noted in Section 1.3, is generally defined by $${y_n} = \sum\limits_{i = 0}^M {{a_i}{u_{n - i}}} - \sum\limits_{i = 1}^N {{b_i}{y_{n - i}}} $$ (5.1) where {u n } is the input sequence, {y n } is the output sequence, and a i , and b i are some constants.
Robert King +4 more
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On fixed-point roundoff error analysis
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1989The author points out the existence of work published by the author (US Dept. of Commerce, Tech. Rep. AD-A086826, 57 pp., Apr. 1980) prior to the appearance of the paper by Barnes et al. (ibid., vol.ASSP-33, p.595-606, June 1985) covering the same subject. >
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Tests of probabilistic models for propagation of roundoff errors
Communications of the ACM, 1966In 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, 1974Generalized 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, 1998We 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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