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Approximate testing with relative error

1999
*
Proceedings of the thirty-first annual ACM symposium on Theory of computing - STOC '99
*

This work considers

doi:10.1145/301250.301269
dblp:conf/stoc/KiwiMS99
fatcat:nwskgp3xcbf2rc4w7bxofhv2f4
*approximation**errors*whose magnitude grows*with*the size of the input to the program. ... We formalize the notion and initiate the investigation of*approximate**testing*for arbitrary forms of the*error*term. ...*Testing**with**Relative**Error*In this section we show how to put together the results derived so far and obtain*approximate**relative**error*testers. First, we introduce some basic terminology. ...##
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Approximate testing with error relative to input size

2003
*
Journal of computer and system sciences (Print)
*

This work considers

doi:10.1016/s0022-0000(03)00004-7
fatcat:dexcmsh2ofayvgabrv3cr5hbom
*approximation**errors*whose magnitude grows*with*the size of the input to the program. ... We formalize the notion and initiate the investigation of*approximate**testing*for arbitrary forms of the*error*term. ... In Section 4, we extend the*approximate*self-testers definition of [11, 15] in order to capture the idea of*approximate*self-*testing**with**relative**error*. ...##
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A New Approximate Adder with Low Relative Error and Correct Sign Calculation

2015
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Design, Automation & Test in Europe Conference & Exhibition (DATE), 2015
*
unpublished

Compared to the existing

doi:10.7873/date.2015.0627
fatcat:y3tww4k6zjalbffvwpy3r2qryy
*approximate*adders, our adder significantly reduces the maximal*relative**error*and ensures correct sign calculation*with*comparable area, delay, and power consumption. ... However, existing*approximate*adders rarely control the*relative**error*and the potential sign*error*of the calculation results. ... Thus, the maximal*relative**error*of our proposed*approximate*adder*with**error*reduction is 1 2 k . C. ...##
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Approximate Flow Friction Factor: Estimation of the Accuracy Using Sobol's Quasi-Random Sampling

2022
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Axioms
*

The ability of the Sobol quasi-random vs. random distribution of

doi:10.3390/axioms11020036
fatcat:buslkmvgizaw3nvjgpkyld3kk4
*testing*points to capture the maximal*relative**error*using a sufficiently small number of samples is evaluated. ... To avoid picking points*with*undetected*errors*, a sufficient minimal number of such points should be chosen, and they should be distributed using proper patterns. ... Compared*with*the methodology by Brkić [14]*with*740 quasi-uniform*testing*points*with*the*error*estimated up to 0.00120421%, Sobol's quasi-random*testing*captured an even higher*error*of 0.00120432% ...##
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Multi-linearity Self-Testing with Relative Error
[chapter]

2000
*
Lecture Notes in Computer Science
*

We investigate self-

doi:10.1007/3-540-46541-3_25
fatcat:alwynu2dbze4foa2y7foodx2y4
*testing*programs*with**relative**error*by allowing*error*terms proportional to the function to be computed. ... We construct new self-testers*with**relative**error*for real-valued multi-linear functions defined over finite rational domains. ...*Testing**with**relative**error*In this section we show how our results lead to*approximate*self-testers*with**relative**error*for both linear functions and multi-linear functions. ...##
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Multi-Linearity Self-Testing with Relative Error

2004
*
Theory of Computing Systems
*

We investigate self-

doi:10.1007/s00224-004-1125-y
fatcat:a6gxocslavaj5inylr7b7midr4
*testing*programs*with**relative**error*by allowing*error*terms proportional to the function to be computed. ... We construct new self-testers*with**relative**error*for real-valued multi-linear functions defined over finite rational domains. ...*Testing**with**relative**error*In this section we show how our results lead to*approximate*self-testers*with**relative**error*for both linear functions and multi-linear functions. ...##
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Design of Antenna with Low Intensity RFID Wireless Network Signal

2016
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International Journal of Future Generation Communication and Networking
*

chamber which is distributed as superposed field of multiple columns plane wave, make an analytical calculation on

doi:10.14257/ijfgcn.2016.9.10.03
fatcat:sxdrputo6zb2fc26lclrkpozgi
*relative**error*, which can be controlled within 3%, of selected*test*point to satisfy ...*Testing*direction and*relative*distance nearest to*test*position of environmental field intensity are analyzed using simulating calculation, taking three-dimensional cube good conductor as general*test*... . 678 Variation of*Relative**Error*Along*With**Relative*Distance When the Oblique Incidence Occurs Simulated Reverberation Chamber Environment of Multi-Variation of*Relative**Error*of*Test*Point Along*With*...##
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Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data
[article]

2017
*
arXiv
*
pre-print

This paper develops a new algorithm for fixed-rank psd

arXiv:1706.05736v1
fatcat:oeye7rs7hzfexk3b3fkaldmgva
*approximation*from a sketch. The approach combines the Nystrom*approximation**with*a novel mechanism for rank truncation. ... Theoretical analysis establishes that the proposed method can achieve any prescribed*relative**error*in the Schatten 1-norm and that it exploits the spectral decay of the input matrix. ... We evaluate the performance using the*relative**error*metric: Schatten p-norm*relative**error*= A −Â r p A − A r p − 1. (5.1) We perform 20 independent trials and report the average*error*. ...##
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Auxiliary basis sets for density fitting–MP2 calculations: Nonrelativistic triple-ζ all-electron correlation consistent basis sets for the 3d elements Sc–Zn

2008
*
Journal of Chemical Physics
*

The

doi:10.1063/1.2826348
pmid:18247927
fatcat:dgsi2vmjcvftbcdpf3mrxy6zjy
*relative**error*in using these auxiliary basis sets is found to be around four orders of magnitude smaller than that from utilizing triple-orbital basis sets rather than corresponding quadruple-basis ... sets, in calculation of the correlation energy for a*test*set of 54 small to medium sized transition metal complexes. ... III*Relative*percentage*errors*introduced via the density fitting*approximation*for a*test*set of 54 molecules containing 3d transition metal elements. ...##
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Efficient estimation of probabilities in thet distribution

1987
*
Behavoir research methods, instruments & computers
*

Instead,

doi:10.3758/bf03205616
fatcat:vmsg65ly4vfxrc2t7zlupwjphq
*test*values of p correspondingto the t values were computed by Table 3 3 Performance of*Approximations**with*Selected Values of t Percentage*Approximation*Estimated p Absolute*Error**Relative*... The accuracy of Gaver and Kafadar's (1984)*approximation*varies substantially*with*the level of p, but its*relative**error*is low. ...##
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Conditional properties of unconditional parametric bootstrap procedures for inference in exponential families

2008
*
Biometrika
*

A bootstrap procedure which ignores the conditioning 1 is shown to have desirable conditional properties, in providing third-order

doi:10.1093/biomet/asn011
fatcat:szh42nwqgzbcvmabtustokunhi
*relative*accuracy in*approximation*of p-values associated*with*the optimal ... The optimal*test*which is*approximated*is a conditional one, based on conditioning on the sufficient statistic for the nuisance parameter. ...*with**relative**error*of order O(n −3/2 ). ...##
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Colebrook's Flow Friction Explicit Approximations Based on Fixed-Point Iterative Cycles and Symbolic Regression

2019
*
Computation
*

Despite the starting point using a simple rational function, it reduces the

doi:10.3390/computation7030048
fatcat:e6ktyo2xrzehjoocjpbktezzka
*relative**error*of the*approximation**with*one internal cycle from 1.81% to 0.156% (i.e., by a factor of 11.6), whereas the*relative*...*error*of the*approximation**with*two internal cycles is reduced from 0.317% to 0.0259% (i.e., by a factor of 12.24). ...*Rel*.*Error*% 740*Test*Points 1 2 Million*Test*Point 2 Re from 10 4 to 10 8 .2Reynolds number Re from 4000 to 10 8 . ...##
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Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks

2021
*
Journal of Scientific Computing
*

We use various methods to establish comparability between

doi:10.1007/s10915-021-01532-w
fatcat:s4ygybankvbvxctuwemykffzgm
*test*-cases by minimizing the effect of the choice of*test*-cases on the optimization and sampling aspects of the learning problem. ... Turning to practically more successful and modern architectures, at the end of this study we derive improved*error*bounds by focusing on convolutional neural networks. ... for [T3-V]*with*p = 50 and different shifts μ Fig. 17 17 Plot of the mean*relative*training and*test**error*for [T3-V]*with*p = 50 and μ = 10 −4 Fig. 18 Plot of the mean*relative*training and*test**error*...##
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Fast Taylor polynomial evaluation for the computation of the matrix cosine

2019
*
Journal of Computational and Applied Mathematics
*

It is based on recent new matrix polynomial evaluation methods for the Taylor

doi:10.1016/j.cam.2018.12.041
fatcat:7jjhcs3zvzcxlapzixp3cvv2au
*approximation*and a mixed forward and backward*error*analysis. ... The matrix polynomial evaluation methods allow to evaluate the Taylor polynomial*approximation*of the matrix cosine function more e ciently than using Paterson-Stockmeyer method. ... Figure 1 : 1 Experimental results for*Test*1. Normwise*relative**errors*. Ratio of matrix products. Figure 2 : 2 Experimental results for*Test*2. Normwise*relative**error*. ...##
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Variational training of neural network approximations of solution maps for physical models
[article]

2019
*
arXiv
*
pre-print

Table 4 presents the

arXiv:1905.02789v1
fatcat:st7m6wzlpndfnkinodxs75mcje
*relative**errors*for different N train and N*test**with*K " 5. The*test**relative**error*decreases as N train increases. ... Table 1 and Table 2 present the number of epoches, train loss,*test*loss, train*relative**error*, and*test**relative**error*for the first three H-matrices*with*N train " 10000 and N train " 4000 respectively ...
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