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Reducing computational roundoff errors efficiently

Computers & Operations Research, 1974
Edward L. Melnick
semanticscholar   +2 more sources

A Warning of Roundoff Errors in Regression

The American Statistician, 1963
R. Freund
semanticscholar   +2 more sources

Calculator Calculus and Roundoff Errors.

The American Mathematical Monthly, 1980
G. Miel
semanticscholar   +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 Babuska, Gustaf Söderlind
openaire   +1 more source

Algorithms for roundoff error analysis —A relative error approach

Computing, 1980
Methods 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
openaire   +1 more source

Synthesis Methodology of AW filters for RF applications based on Matrix Rotations to overcome round-off errors

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
semanticscholar   +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. >
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A roundoff error analysis of the Oja's subspace rule

1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2002
This 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

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.
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