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Roundoff error analysis of the PCA networks
IEEE Instrumentation and Measurement Technology Conference Sensing, Processing, Networking. IMTC Proceedings, 2002This paper deals with some of the effects of finite precision data representation and arithmetics in principal component analysis (PCA) neural networks. The PCA networks are single layer linear neural networks that use some versions of Oja's learning rule.
T. Szabo, G. Horvath
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Limit distribution of a roundoff error
Statistics & Probability Letters, 2012Denote by \([x]:=\sup\{m\in\mathbb{Z}:\,m\leq x\}\) the integral part of \(x\in\mathbb{R}\) and by \(\{x\}:=x-[x]\in[0,1)\) its fractional part. Let \(X\) be a random variable. The conditional distribution function \(F_n(x):=P(\{X\}\leq x \mid [X]=n)\) for an integer \(n\in\mathbb{N}\) is investigated. Characterizations of the limit of \(F_n\) when \(n\
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Roundoff Error and Double Precision
1977As we have seen, most applications of computers to calculus involve the evaluation of several terms in a sequence. The evaluations continue until some criterion is satisfied. In Figure 1–5 for example, the criterion was that the terms of two sequences differ by less than 10-3. In EXERCISE 5–5 the values of the sequence \( \frac{{f(1.8 + {{10}^{{ - n}}})
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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.
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Roundoff errors in floating-point summation
BIT, 1975All possible schemes for the calculation of the sum ofn addends by means ofn−1 floating-point additions is considered and in case of positive addends it is shown how to use the Huffman algorithm to choose a scheme to obtain the least upper bound on the accumulated roundoff error in the result.
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Efficient Calculation of the Effects of Roundoff Errors
ACM Transactions on Mathematical Software, 1978John L. Larson, Ahmed H. Sameh
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On the calculation of the effects of roundoff errors
ACM Transactions on Mathematical Software, 1981openaire +3 more sources
Stairway to Heaven: Accumulation of Roundoff Error
1996Martin Gardner’s popular “Mathematical Games” column appeared monthly in Scientific American from January 1957 through December 1981. During those 25 years he entertained his readers with discussions of such topics as how to fold adding machine tape into hexaflexagons, John Conway’s Game of Life, and the discoveries of the mysterious numerologist Dr ...
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