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Reducing computational roundoff errors efficiently
Computers & Operations Research, 1974Edward L. Melnick
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A Warning of Roundoff Errors in Regression
The American Statistician, 1963R. Freund
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Calculator Calculus and Roundoff Errors.
The American Mathematical Monthly, 1980G. Miel
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On Roundoff Error Growth in Elliptic Problems
ACM Transactions on Mathematical Software, 2018Large-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 Babuska, Gustaf Söderlind
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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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IUS, 2021
Filtering synthesis methodologies have become increasingly popular among AW filter designers due to their effectiveness, precision, and usefulness. Regardless of dealing with an equivalent Butterworth-Van Dyke electrical or coupling-nodal model, current ...
L. Acosta +4 more
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Filtering synthesis methodologies have become increasingly popular among AW filter designers due to their effectiveness, precision, and usefulness. Regardless of dealing with an equivalent Butterworth-Van Dyke electrical or coupling-nodal model, current ...
L. Acosta +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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A roundoff error analysis of the Oja's subspace rule
1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2002This 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
1998One 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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