Results 131 to 140 of about 7,840 (182)

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.
Kaneko, Toyohisa, Liu, Bede
openaire   +2 more sources

A new iterative refinement with roundoff error analysis

Numerical Linear Algebra with Applications, 2011
AbstractIn 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
Wu, Xinyuan, Wang, Zhengyu
openaire   +2 more sources

Guaranteed state estimation accuracies with roundoff error

29th IEEE Conference on Decision and Control, 1990
Kalman filter theory is modified to accommodate roundoff errors in state computation. Two problems are solved: (i) choosing the wordlength required for each state computation to guarantee specified estimation accuracies of multiple output variables of interest; and (ii) finding the minimal variance estimator subject to inequality constraints on ...
R.E. Skelton, D. Williamson
openaire   +1 more source

Roundoff errors in floating-point summation

BIT, 1975
All 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.
openaire   +2 more sources

Roundoff error analysis of the PCA networks

IEEE Instrumentation and Measurement Technology Conference Sensing, Processing, Networking. IMTC Proceedings, 2002
This 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
openaire   +1 more source

Impact of roundoff errors in LDPC decoding

2008 3rd International Symposium on Wireless Pervasive Computing, 2008
In 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.
N. Kanistras, V. Paliouras
openaire   +1 more source

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.
openaire   +1 more source

Limit distribution of a roundoff error

Statistics & Probability Letters, 2012
Denote 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\
openaire   +2 more sources

On Roundoff Error Growth in Elliptic Problems

ACM Transactions on Mathematical Software, 2018
Large-scale linear systems arise in finite-difference and finite-element discretizations of elliptic problems. With increasing computer performance, ever larger systems are solved using direct methods. How large can such systems be without roundoff compromising accuracy? Here we model roundoff dynamics in standard LU
Ivo Babuška, Gustaf Söderlind
openaire   +1 more source

On fixed-point roundoff error analysis

IEEE Transactions on Acoustics, Speech, and Signal Processing, 1989
The 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. >
openaire   +1 more source