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Approximate testing with relative error

Marcos Kiwi, Frédéric Magniez, Miklos Santha
1999 Proceedings of the thirty-first annual ACM symposium on Theory of computing - STOC '99  
This work considers 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.  ... 
doi:10.1145/301250.301269 dblp:conf/stoc/KiwiMS99 fatcat:nwskgp3xcbf2rc4w7bxofhv2f4

Approximate testing with error relative to input size

Marcos Kiwi, Frédéric Magniez, Miklos Santha
2003 Journal of computer and system sciences (Print)  
This work considers 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.  ... 
doi:10.1016/s0022-0000(03)00004-7 fatcat:dexcmsh2ofayvgabrv3cr5hbom

A New Approximate Adder with Low Relative Error and Correct Sign Calculation

Weikang Qian, Junjun Hu
2015 Design, Automation & Test in Europe Conference & Exhibition (DATE), 2015   unpublished
Compared to the existing 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.  ... 
doi:10.7873/date.2015.0627 fatcat:y3tww4k6zjalbffvwpy3r2qryy

Approximate Flow Friction Factor: Estimation of the Accuracy Using Sobol's Quasi-Random Sampling

Pavel Praks, Dejan Brkić
2022 Axioms  
The ability of the Sobol quasi-random vs. random distribution of 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%  ... 
doi:10.3390/axioms11020036 fatcat:buslkmvgizaw3nvjgpkyld3kk4

Multi-linearity Self-Testing with Relative Error [chapter]

Frédéric Magniez
2000 Lecture Notes in Computer Science  
We investigate self-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.  ... 
doi:10.1007/3-540-46541-3_25 fatcat:alwynu2dbze4foa2y7foodx2y4

Multi-Linearity Self-Testing with Relative Error

Frédéric Magniez
2004 Theory of Computing Systems  
We investigate self-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.  ... 
doi:10.1007/s00224-004-1125-y fatcat:a6gxocslavaj5inylr7b7midr4

Design of Antenna with Low Intensity RFID Wireless Network Signal

Zheng Juan, Gu Juanjuan
2016 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 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  ... 
doi:10.14257/ijfgcn.2016.9.10.03 fatcat:sxdrputo6zb2fc26lclrkpozgi

Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data [article]

Joel A. Tropp, Alp Yurtsever, Madeleine Udell, Volkan Cevher
2017 arXiv   pre-print
This paper develops a new algorithm for fixed-rank psd 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.  ... 
arXiv:1706.05736v1 fatcat:oeye7rs7hzfexk3b3fkaldmgva

Auxiliary basis sets for density fitting–MP2 calculations: Nonrelativistic triple-ζ all-electron correlation consistent basis sets for the 3d elements Sc–Zn

J. Grant Hill, James A. Platts
2008 Journal of Chemical Physics  
The 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.  ... 
doi:10.1063/1.2826348 pmid:18247927 fatcat:dgsi2vmjcvftbcdpf3mrxy6zjy

Efficient estimation of probabilities in thet distribution

Alfred L. Brophy
1987 Behavoir research methods, instruments & computers  
Instead, 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.  ... 
doi:10.3758/bf03205616 fatcat:vmsg65ly4vfxrc2t7zlupwjphq

Conditional properties of unconditional parametric bootstrap procedures for inference in exponential families

T. J. DiCiccio, G. A. Young
2008 Biometrika  
A bootstrap procedure which ignores the conditioning 1 is shown to have desirable conditional properties, in providing third-order 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 ).  ... 
doi:10.1093/biomet/asn011 fatcat:szh42nwqgzbcvmabtustokunhi

Colebrook's Flow Friction Explicit Approximations Based on Fixed-Point Iterative Cycles and Symbolic Regression

Dejan Brkić, Pavel Praks
2019 Computation  
Despite the starting point using a simple rational function, it reduces the 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 .  ... 
doi:10.3390/computation7030048 fatcat:e6ktyo2xrzehjoocjpbktezzka

Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks

Moritz Geist, Philipp Petersen, Mones Raslan, Reinhold Schneider, Gitta Kutyniok
2021 Journal of Scientific Computing  
We use various methods to establish comparability between 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  ... 
doi:10.1007/s10915-021-01532-w fatcat:s4ygybankvbvxctuwemykffzgm

Fast Taylor polynomial evaluation for the computation of the matrix cosine

Jorge Sastre, Javier Ibáñez, Pedro Alonso-Jordá, Jesús Peinado, Emilio Defez
2019 Journal of Computational and Applied Mathematics  
It is based on recent new matrix polynomial evaluation methods for the Taylor 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.  ... 
doi:10.1016/j.cam.2018.12.041 fatcat:7jjhcs3zvzcxlapzixp3cvv2au

Variational training of neural network approximations of solution maps for physical models [article]

Yingzhou Li, Jianfeng Lu, Anqi Mao
2019 arXiv   pre-print
Table 4 presents the 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  ... 
arXiv:1905.02789v1 fatcat:st7m6wzlpndfnkinodxs75mcje
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