On a special case of the two-variable Newton interpolation polynomial

Varsamis, Dimitris; Karampetakis, Nicholas P.

doi:10.1109/ccca.2012.6417866

Cited by 5 publications

(6 citation statements)

References 16 publications

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“…In practice, the bivariate Newton interpolation function can be further simplified with the rectangular basis of equidistant interpolation points suggested by Varsamis and Karampetakis [25]. After the interpolation process, the training data will then be fed into a five-layer NN.…”

Section: By Substituting the Derived Variance Andmentioning

confidence: 99%

Wi-Counter: Smartphone-Based People Counter Using Crowdsourced Wi-Fi Signal Data

Chan

Guo

et al. 2015

IEEE Trans. Human-Mach. Syst.

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Reliable people counting is crucial to many urban applications. However, most existing people counting systems are sensor-based and can only work in some fixed gateways or checkpoints where sensors have been installed. This high dependence on the exact locations of sensors leads to low accuracy. To overcome these limitations, in this paper, we propose a smartphone-based people counting system, Wi-Counter, by leveraging the pervasive Wi-Fi infrastructure. To collect comprehensive Wi-Fi signals and people count information based on crowdsource, Wi-Counter first adopts a preprocessor to overcome the noisy, discrepant, and fragile data based on the Wiener filter and Newton interpolation. It then makes use of the designated five-layer neural network to learn the relation model between the Wi-Fi signals and the number of people. By analyzing the received Wi-Fi signals, Wi-Counter can estimate the number of people based on the resulting model. We have conducted experiments by implementing a prototype of Wicounter based on smartphones and evaluated the system in terms of accuracy and power consumption in an indoor testbed covering an area of 96 m 2 . Wi-Counter achieved a counting accuracy of up to 93% and exhibited reliable and robust performance resisting temporal environmental changes with negligible power usage.

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Section: By Substituting the Derived Variance Andmentioning

confidence: 99%

Wi-Counter: Smartphone-Based People Counter Using Crowdsourced Wi-Fi Signal Data

Chan

Guo

et al. 2015

IEEE Trans. Human-Mach. Syst.

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“…where n is the total degree of the bivariate polynomial. An algorithm for the computation of the above polynomial is given (a) in [11] which is applied to random interpolation points in a triangular basis and (b) in [10] which is applied in the special case of equidistant interpolation points. The recursive type for the equidistant interpolation points is given by…”

Section: Two-variable Newton Interpolationmentioning

confidence: 99%

“…In this paper, we start by presenting in Section 2, the way that the Newton bivariate interpolation method in [10] is applied to equidistant points with aim to simplify the implementation. The numerical algorithmic implementation of the Newton bivariate interpolation method is given, by three alternative methods.…”

Section: Introductionmentioning

confidence: 99%

On the numerical computation of the determinant of a bivariate polynomial matrix

Varsamis¹,

Karampetakis²

2015

ams

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The paper, based on the technique evaluation-interpolation, proposes a new numerical algorithm for the computation of the determinant of a bivariate polynomial matrix. The numerical algorithm uses the Newton bivariate polynomial interpolation with equidistant points. The algorithm is applied to the programming environment of MATLAB and is compared to the corresponding build-in function of MATLAB det() which uses symbolic operations.

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“…The formula is given by Eqs. (13) and (14). (13) (14) In analyzing the missing data, the cases are first ordered according to data size.…”

Section: Nrmsementioning

confidence: 99%

“…This is because random data requires finding an approximate function to use in place of a more complicated function. This method is distinguished by a degree of continuity [13][14][15]. Estimating the function used for data collection requires estimating the unknown parameters at each point of interest using values obtained from measurements.…”

Section: Related Workmentioning

confidence: 99%

Imputation of Medical Data Using Subspace Condition Order Degree Polynomials

Silachan¹,

Tantatsanawong²

2014

Journal of Information Processing Systems

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Abstract-Temporal medical data is often collected during patient treatments that require personal analysis. Each observation recorded in the temporal medical data is associated with measurements and time treatments. A major problem in the analysis of temporal medical data are the missing values that are caused, for example, by patients dropping out of a study before completion. Therefore, the imputation of missing data is an important step during pre-processing and can provide useful information before the data is mined. For each patient and each variable, this imputation replaces the missing data with a value drawn from an estimated distribution of that variable. In this paper, we propose a new method, called Newton's finite divided difference polynomial interpolation with condition order degree, for dealing with missing values in temporal medical data related to obesity. We compared the new imputation method with three existing subspace estimation techniques, including the k-nearest neighbor, local least squares, and natural cubic spline approaches. The performance of each approach was then evaluated by using the normalized root mean square error and the statistically significant test results. The experimental results have demonstrated that the proposed method provides the best fit with the smallest error and is more accurate than the other methods.

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On a special case of the two-variable Newton interpolation polynomial

Cited by 5 publications

References 16 publications

Wi-Counter: Smartphone-Based People Counter Using Crowdsourced Wi-Fi Signal Data

Wi-Counter: Smartphone-Based People Counter Using Crowdsourced Wi-Fi Signal Data

On the numerical computation of the determinant of a bivariate polynomial matrix

Imputation of Medical Data Using Subspace Condition Order Degree Polynomials

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