Notes on spline functions IV: A cardinal spline analogue of the theorem of the brothers Markov

1973 ◽  
Vol 16 (1) ◽  
pp. 94-102 ◽  
Author(s):  
F. B. Richards ◽  
I. J. Schoenberg
Keyword(s):  
Spline Functions ◽  
Cardinal Spline

scholarly journals The Cardinal Spline Methods for the Numerical Solution of Nonlinear Integral Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xiaoyan Liu ◽  
Jin Xie ◽  
Zhi Liu ◽  
Jiahuan Huang
Keyword(s):  
Integral Equations ◽  
High Accuracy ◽  
Spline Functions ◽  
Sufficient Condition ◽  
Nonlinear Integral Equations ◽  
Effective Technique ◽  
Original Solution ◽  
Cardinal Spline ◽  
The Matrix ◽  
Cardinal Splines

In this study, an effective technique is presented for solving nonlinear Volterra integral equations. The method is based on application of cardinal spline functions on small compact supports. The integral equation is reduced to a system of algebra equations. Since the matrix for the system is triangular, it is relatively straightforward to solve for the unknowns and an approximation of the original solution with high accuracy is accomplished. Several cardinal splines are employed in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined, and the convergence rate is analyzed. We compare our method with other methods proposed in recent papers and demonstrated the advantage of our method with several examples.

Identification of MIMO Hammerstein systems using cardinal spline functions

2006 ◽  
Vol 16 (7) ◽  
pp. 659-670 ◽  
Author(s):  
Kwong Ho Chan ◽  
Jie Bao ◽  
William J. Whiten
Keyword(s):  
Spline Functions ◽  
Hammerstein Systems ◽  
Cardinal Spline

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.

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