Construction and Applications of Hermite Interpolating Quadratic Spline Functions of two and three Variables

1985 ◽  
pp. 232-252
Author(s):  
Gerhard Heindl
Keyword(s):  
Spline Functions ◽  
Quadratic Spline

Analysis of switched quantizer based on the quadratic spline functions

2017 ◽  
Vol 94 (12) ◽  
pp. 2348-2355
Author(s):  
Zoran Peric ◽  
Jelena Nikolic ◽  
Lazar Velimirovic ◽  
Stefan Panic ◽  
Miomir Stankovic
Keyword(s):  
Spline Functions ◽  
Quadratic Spline

scholarly journals Solution of Thermoelectricity Problems Energy Method

2018 ◽  
Vol 38 ◽  
pp. 04002
Author(s):  
Muheyat Niyazbek ◽  
M.O Nogaybaeva ◽  
Kuenssaule Talp ◽  
A.A Kudaikulov
Keyword(s):  
Heat Transfer ◽  
Heat Flow ◽  
Energy Method ◽  
Local Heat ◽  
Spline Functions ◽  
Quadratic Spline ◽  
Conservation Of Energy ◽  
Computing Algorithm ◽  
Limited Length ◽  
Flow Heat

On the basis of the fundamental laws of conservation of energy in conjunction with local quadratic spline functions was developed a universal computing algorithm, a method and associated software, which allows to investigate the Thermophysical insulated rod, with limited length, influenced by local heat flow, heat transfer and temperature

scholarly journals Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3182
Author(s):  
Gabriela Cristescu ◽  
Vlad-Florin Drăgoi ◽  
Sorin Horaţiu Hoară
Keyword(s):  
Generalized Convexity ◽  
Low Complexity ◽  
Small Error ◽  
Spline Functions ◽  
Shape Preserving ◽  
Quadratic Spline ◽  
Minimal Network ◽  
Convexity Properties ◽  
Minimal Networks ◽  
Accuracy Of Approximation

Some properties of generalized convexity for sets and functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is developed based on their mutual complementarity properties. The approximating objects are from the class of quadratic spline functions, constructed based on both interpolation conditions and shape knowledge. It is proved that the approximant objects preserve both the high-order convexity and some extremum properties of the exact reliability polynomials. It leads to pointing out the area of the network where the maximum number of paths is achieved. Numerical examples and simulations show the performance of the algorithm, both in terms of low complexity, small error and shape preserving. Possibilities of increasing the accuracy of approximation are discussed.

On the approximation of $ \ exp (-x) $ on the half-axis by spline functions in three-point rational interpolants

2019 ◽  
pp. 32-37
Author(s):  
Abdul-Rashid Ramazanov ◽  
V.G. Magomedova
Keyword(s):  
Convergence Rate ◽  
Spline Functions ◽  
Rational Spline ◽  
Rational Interpolants ◽  
Half Axis

For the function $f(x)=\exp(-x)$, $x\in [0,+\infty)$ on grids of nodes $\Delta: 0=x_0<x_1<\dots $ with $x_n\to +\infty$ we construct rational spline-functions such that $R_k(x,f, \Delta)=R_i(x,f)A_{i,k}(x)\linebreak+R_{i-1}(x, f)B_{i,k}(x)$ for $x\in[x_{i-1}, x_i]$ $(i=1,2,\dots)$ and $k=1,2,\dots$ Here $A_{i,k}(x)=(x-x_{i-1})^k/((x-x_{i-1})^k+(x_i-x)^k)$, $B_{i,k}(x)=1-A_{i,k}(x)$, $R_j(x,f)=\alpha_j+\beta_j(x-x_j)+\gamma_j/(x+1)$ $(j=1,2,\dots)$, $R_j(x_m,f)=f(x_m)$ при $m=j-1,j,j+1$; we take $R_0(x,f)\equiv R_1(x,f)$. Bounds for the convergence rate of $R_k(x,f, \Delta)$ with $f(x)=\exp(-x)$, $x\in [0,+\infty)$, are found.

PREDICTING CHARACTERISTICS OF SELF SIMILAR TRAFFIC BY SPLINE-EXTRAPOLATION

2019 ◽  
Author(s):  
Irina Strelkovskay ◽  
Irina Solovskaya ◽  
Anastasija Makoganjuk ◽  
Nikolaj Severin
Keyword(s):  
Quality Characteristics ◽  
Traffic Prediction ◽  
Normative Values ◽  
Spline Functions ◽  
Network Nodes ◽  
Traffic Forecasting ◽  
Network Equipment ◽  
Self Similar ◽  
Accuracy Of Prediction

The problem of forecasting self-similar traffic, which is characterized by a considerable number of ripples and the property of long-term dependence, is considered. It is proposed to use the method of spline extrapolation using linear and cubic splines. The results of self-similar traffic prediction were obtained, which will allow to predict the necessary size of the buffer devices of the network nodes in order to avoid congestion in the network and exceed the normative values ​​of QoS quality characteristics. The solution of the problem of self-similar traffic forecasting obtained with the Simulink software package in Matlab environment is considered. A method of extrapolation based on spline functions is developed. The proposed method has several advantages over the known methods, first of all, it is sufficient ease of implementation, low resource intensity and accuracy of prediction, which can be enhanced by the use of quadratic or cubic interpolation spline functions. Using the method of spline extrapolation, the results of self-similar traffic prediction were obtained, which will allow to predict the required volume of buffer devices, thereby avoiding network congestion and exceeding the normative values ​​of QoS quality characteristics. Given that self-similar traffic is characterized by the presence of "bursts" and a long-term dependence between the moments of receipt of applications in this study, given predetermined data to improve the prediction accuracy, it is possible to use extrapolation based on wavelet functions, the so-called wavelet-extrapolation method. Based on the results of traffic forecasting, taking into account the maximum values ​​of network node traffic, you can give practical guidance on how traffic is redistributed across the network. This will balance the load of network objects and increase the efficiency of network equipment.

Smoothing Surface Data by Spline Functions.

1985 ◽  
Author(s):  
P. C. Stein ◽  
W. L. White
Keyword(s):  
Spline Functions ◽  
Surface Data
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