scholarly journals Dynamic Harmonic Synchrophasor Estimator Based on Sinc Interpolation Functions

2019 ◽  
Vol 68 (9) ◽  
pp. 3054-3065 ◽  
Author(s):  
Lei Chen ◽  
Wei Zhao ◽  
Qing Wang ◽  
Fuping Wang ◽  
Songling Huang
Keyword(s):  
Sinc Interpolation ◽  
Interpolation Functions

The Unifying Theory Embraces Lagrange and Sinc Interpolation Functions

2009 ◽  
pp. 353-370
Author(s):  
Carlo Ciulla
Keyword(s):  
Mathematical Formulation ◽  
Linear Functions ◽  
Interpolation Error ◽  
Upper And Lower Bounds ◽  
The Novel ◽  
B Splines ◽  
Sinc Interpolation ◽  
Sampling Locations ◽  
Interpolation Functions

This chapter is devoted to the mathematics of the Lagrange and Sinc SRE-based interpolation functions. The organization of the text of this chapter is consistent with that of chapters VII, X, and XIV. The basic aim of this chapter is to employ the methodology outlined in the book such to develop a mathematical formulation that allows interpolation error improvement also for Lagrange and Sinc interpolation functions. This is achieved through two instruments that bridge classic interpolation with the present innovative theory. The instruments are the Intensity-Curvature Functional (?E) and the Sub-pixel Efficacy Region (SRE). Math processes are thus presented that start from the calculation of the intensitycurvature terms and the corresponding Intensity-Curvature Functional, determine the SRE and employ the formula of the unifying theory (see equations [16] and [38] for Lagrange and Sinc respectively) to calculate the novel re-sampling locations for the two model interpolation functions. A section of this chapter is delegated to recall to the reader the characterization of upper and lower bounds of interpolation error improvement and interpolation error respectively. Details of this section are reported elsewhere (Ciulla & Deek, 2006). Finally the theoretical presentation of resilient interpolation is extended also to Lagrange and Sinc as it was already presented for the two linear functions and the two B-Splines that were object of treatise in Parts II, III and IV of this book. Although the logic behind the math of resilient interpolation is explained and characterized, resilient interpolation remains in this book a theoretical conceptualization which looks forward to empirical confirmation.

The Results of the Sub-Pixel Efficacy Region Based Lagrange and Sinc Interpolation Functions

2009 ◽  
pp. 371-470
Author(s):  
Carlo Ciulla
Keyword(s):  
One Dimensional ◽  
B Splines ◽  
Sinc Interpolation ◽  
Interpolation Functions

This chapter presents results obtained processing the MRI dataset with classic and SRE-based models of one dimensional Lagrange and Sinc interpolation functions. The presentation is consistent with chapters VIII, XI, and XV where bivariate linear, trivariate linear and B-Splines’ results were reported and consists of a compilation that is both quantitative and qualitative.

scholarly journals A Concretization of an Approximation Method for Non-Affine Fractal Interpolation Functions

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 767
Author(s):  
Alexandra Băicoianu ◽  
Cristina Maria Păcurar ◽  
Marius Păun
Keyword(s):  
Approximation Method ◽  
Finite System ◽  
Countable System ◽  
Fractal Interpolation ◽  
Interpolation Function ◽  
Finite Systems ◽  
Fractal Interpolation Function ◽  
Fractal Interpolation Functions ◽  
Finite Set ◽  
Interpolation Functions

The present paper concretizes the models proposed by S. Ri and N. Secelean. S. Ri proposed the construction of the fractal interpolation function(FIF) considering finite systems consisting of Rakotch contractions, but produced no concretization of the model. N. Secelean considered countable systems of Banach contractions to produce the fractal interpolation function. Based on the abovementioned results, in this paper, we propose two different algorithms to produce the fractal interpolation functions both in the affine and non-affine cases. The theoretical context we were working in suppose a countable set of starting points and a countable system of Rakotch contractions. Due to the computational restrictions, the algorithms constructed in the applications have the weakness that they use a finite set of starting points and a finite system of Rakotch contractions. In this respect, the attractor obtained is a two-step approximation. The large number of points used in the computations and the graphical results lead us to the conclusion that the attractor obtained is a good approximation of the fractal interpolation function in both cases, affine and non-affine FIFs. In this way, we also provide a concretization of the scheme presented by C.M. Păcurar .

CONSTRUCTING MULTIPLE WAVELET PACKETS WITH FIFS

Fractals ◽  
2001 ◽  
Vol 09 (02) ◽  
pp. 165-169
Author(s):  
GANG CHEN ◽  
ZHIGANG FENG
Keyword(s):  
Multiresolution Analysis ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Scaling Functions ◽  
Wavelet Packet Decomposition ◽  
Fractal Interpolation ◽  
Fractal Interpolation Functions ◽  
Interpolation Functions

By using fractal interpolation functions (FIF), a family of multiple wavelet packets is constructed in this paper. The first part of the paper deals with the equidistant fractal interpolation on interval [0, 1]; next, the proof that scaling functions ϕ1, ϕ2,…,ϕr constructed with FIF can generate a multiresolution analysis of L2(R) is shown; finally, the direct wavelet and wavelet packet decomposition in L2(R) are given.

scholarly journals Rational interpolation of the function |x|α by an extended system of Chebyshev – Markov nodes

2020 ◽  
Vol 55 (4) ◽  
pp. 391-405
Author(s):  
E. A. Rovba ◽  
V. Yu. Medvedeva
Keyword(s):  
Rational Functions ◽  
Rational Interpolation ◽  
Asymptotic Equality ◽  
Fixed Number ◽  
Theoretical Research ◽  
Extended System ◽  
Uniform Approximations ◽  
Upper Estimate ◽  
Interpolation Functions ◽  
Interpolation Nodes

In this paper, we study the approximations of a function |x|α, α > 0 by interpolation rational Lagrange functions on a segment [–1,1]. The zeros of the even Chebyshev – Markov rational functions and a point x = 0 are chosen as the interpolation nodes. An integral representation of an interpolation remainder and an upper bound for the considered uniform approximations are obtained. Based on them, a detailed study is made:a) the polynomial case. Here, the authors come to the famous asymptotic equality of M. N. Hanzburg;b) at a fixed number of geometrically different poles, the upper estimate is obtained for the corresponding uniform approximations, which improves the well-known result of K. N. Lungu;c) when approximating by general Lagrange rational interpolation functions, the estimate of uniform approximations is found and it is shown that at the ends of the segment [–1,1] it can be improved.The results can be applied in theoretical research and numerical methods. 

scholarly journals Effects of longitudinal short-distance constraints on the hadronic light-by-light contribution to the muon $$\mathbf {g-2}$$

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Jan Lüdtke ◽  
Massimiliano Procura
Keyword(s):  
Short Distance ◽  
Independent Method ◽  
Recent Model ◽  
Low Energy ◽  
Muon Anomalous Magnetic Moment ◽  
Distance Constraints ◽  
Independent Information ◽  
Intermediate States ◽  
Model Independent ◽  
Interpolation Functions

AbstractWe present a model-independent method to estimate the effects of short-distance constraints (SDCs) on the hadronic light-by-light contribution to the muon anomalous magnetic moment $$a_\mu ^\text {HLbL}$$ a μ HLbL . The relevant loop integral is evaluated using multi-parameter families of interpolation functions, which satisfy by construction all constraints derived from general principles and smoothly connect the low-energy region with those where either two or all three independent photon virtualities become large. In agreement with other recent model-based analyses, we find that the SDCs and thus the infinite towers of heavy intermediate states that are responsible for saturating them have a rather small effect on $$a_\mu ^\text {HLbL}$$ a μ HLbL . Taking as input the known ground-state pseudoscalar pole contributions, we obtain that the longitudinal SDCs increase $$a_\mu ^\text {HLbL}$$ a μ HLbL by $$(9.1\pm 5.0) \times 10^{-11}$$ ( 9.1 ± 5.0 ) × 10 - 11 , where the isovector channel is responsible for $$(2.6\pm 1.5) \times 10^{-11}$$ ( 2.6 ± 1.5 ) × 10 - 11 . More precise estimates can be obtained with our method as soon as further accurate, model-independent information about important low-energy contributions from hadronic states with masses up to 1–2 GeV become available.

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