Interpolation Functions

1984 ◽  
pp. 109-140 ◽  
Author(s):  
C. A. Brebbia ◽  
J. C. F. Telles ◽  
L. C. Wrobel
Keyword(s):  
Interpolation Functions

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.

scholarly journals Cover interpolation functions and h-enrichment in finite element method

2017 ◽  
Vol 2 (1) ◽  
pp. 72-79
Author(s):  
H. Arzani ◽  
E. Khoshbavar rad ◽  
M. Ghorbanzadeh ◽  
◽  
◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interpolation Functions ◽  
Element Method

Sequential interpolation functions

1976 ◽  
Vol 10 (1) ◽  
pp. 133-143 ◽  
Author(s):  
Raul A. Feijoo ◽  
Luiz Bevilacqua
Keyword(s):  
Interpolation Functions
Sign in / Sign up

Export Citation Format

Share Document