Results 131 to 140 of about 2,905,950 (213)
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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\
Takaaki Shimura
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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
Wu, Xinyuan, Wang, Zhengyu
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Improved Roundoff Error Analysis for Precomputed Twiddle Factors
Journal of Computational Analysis and Applications, 2002The paper presents both worst-case and average case analysis of rounfoff errors occuring in eight precomputation methods of twiddle factors. Two of the methods are new. The paper is interested for methods with small roundoff errors, low complexity and using only little computer memory.
Tasche, Manfred, Zeuner, Hansmartin
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SIAM Journal on Matrix Analysis and Applications, 2019
The roundoff-error-free (REF) LU factorization, along with the REF forward and backward substitution algorithms, allows a rational system of linear equations to be solved exactly and efficiently.
Christopher J. Lourenco +3 more
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The roundoff-error-free (REF) LU factorization, along with the REF forward and backward substitution algorithms, allows a rational system of linear equations to be solved exactly and efficiently.
Christopher J. Lourenco +3 more
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Guard Digits vs. Roundoff Error vs. Overall Uncertainty
The Physics Teacher, 2018Roundoff error is an error. It can be dramatically reduced by the use of additional low-order digits, i.e. guard digits. Although the significant-figures idea in its standard form is incompatible with guard digits, this problem can be neatly solved by ...
J. Denker, Larry K. Smith
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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.
Larson, J. L., Sameh, A. H.
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Numerical chaos, roundoff errors, and homoclinic manifolds
Physical Review Letters, 1993The 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 error in fast Fourier transforms
Proceedings of the IEEE, 1975The finite word length used in the computer causes round-off error in the calculation of Fourier coefficients. When the fast Fourier transform method is used, the statistical mean-square error has been previously determined [3] for the case of the decimation-infrequency algorithm. This letter treats the same problem for the decimation-in-time algorithm.
B. Liu, T. Kaneko
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Roundoff Errors in Signal Averaging Systems
IEEE Transactions on Biomedical Engineering, 1986In 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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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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