Rational spline interpolation preserving the shape of the monotonic data

2002 ◽  
Author(s):  
M. Sarfaz
Keyword(s):  
Spline Interpolation ◽  
Rational Spline

Monotone linear rational spline interpolation

1992 ◽  
Vol 9 (4) ◽  
pp. 313-319 ◽  
Author(s):  
Richard D. Fuhr ◽  
Michael Kallay
Keyword(s):  
Spline Interpolation ◽  
Rational Spline

scholarly journals Wind Velocity Data Interpolation Using Rational Cubic Spline

2018 ◽  
Vol 225 ◽  
pp. 04006
Author(s):  
Samsul Ariffin Bin Abdul Karim ◽  
S. Suresh Kumar Raju
Keyword(s):  
Wind Velocity ◽  
Hermite Polynomial ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
Numerical Results ◽  
Data Interpolation ◽  
Velocity Data ◽  
Cubic Spline Interpolation ◽  
Rational Spline ◽  
The Given

Wind velocity data is always having positive value and the minimum value approximately close to zero. The standard cubic spline interpolation (not-a-knot and natural) as well as cubic Hermite polynomial may be produces interpolating curve with negative values on some subintervals. To cater this problem, a new rational cubic spline with three parameters is constructed. This rational spline will be used to preserve the positivity of the wind velocity data. Numerical results shows that the proposed scheme work very well and give visually pleasing interpolating curve on the given domain.

Low degree rational spline interpolation

1997 ◽  
Vol 37 (4) ◽  
pp. 901-909 ◽  
Author(s):  
Peeter Oja
Keyword(s):  
Spline Interpolation ◽  
Rational Spline ◽  
Low Degree

scholarly journals LINEAR/LINEAR RATIONAL SPLINE INTERPOLATION

2010 ◽  
Vol 15 (4) ◽  
pp. 447-455 ◽  
Author(s):  
Erge Ideon ◽  
Peeter Oja
Keyword(s):  
Spline Interpolation ◽  
Monotone Function ◽  
Uniform Mesh ◽  
Second Derivative ◽  
Numerical Examples ◽  
First Derivative ◽  
Rational Spline ◽  
Smoothness Class ◽  
Class C ◽  
Theoretical Results

For a strictly monotone function y on [a, b] we describe the construction of an interpolating linear/linear rational spline S of smoothness class C 1. We show that for the linear/linear rational splines we obtain ¦S(xi ) − y(xi )¦8 = O(h 4) on uniform mesh xi = a + ih, i = 0,…, n. We prove also the superconvergence of order h3 for the first derivative and of order h2 for the second derivative of S in certain points. Numerical examples support the obtained theoretical results. This work was supported by the Estonian Science Foundation grant 8313.

scholarly journals QUADRATIC/LINEAR RATIONAL SPLINE INTERPOLATION

2013 ◽  
Vol 18 (2) ◽  
pp. 250-259 ◽  
Author(s):  
Erge Ideon ◽  
Peeter Oja
Keyword(s):  
Spline Interpolation ◽  
Concave Function ◽  
Uniform Mesh ◽  
Second Derivative ◽  
Numerical Examples ◽  
First Derivative ◽  
The Third ◽  
Rational Spline ◽  
Smoothness Class ◽  
Third Derivative

We describe the construction of an interpolating quadratic/linear rational spline S of smoothness class C 2 for a strictly convex (or strictly concave) function y on [a, b]. On uniform mesh x i = a + ih, i = 0,..., n, in the case of sufficiently smooth function y the expansions of S and its derivatives are obtained. They give the superconvergence of order h 4 for the first derivative, of order h 3 for the second derivative and of order h 2for the third derivative of S in certain points. Corresponding numerical examples are given.

scholarly journals The Rational Spline Interpolation Based-LOD Method and Its Application to Rotating Machinery Fault Diagnosis

2020 ◽  
Vol 10 (4) ◽  
pp. 1259
Author(s):  
Xiaorui Niu ◽  
Kang Zhang ◽  
Chao Wan ◽  
Xiangmin Chen ◽  
Lida Liao ◽  
...  
Keyword(s):  
Linear Transformation ◽  
Spline Interpolation ◽  
Piecewise Linear ◽  
Rotating Machinery ◽  
Vibration Signals ◽  
Time Frequency ◽  
Rational Spline ◽  
Characteristic Decomposition ◽  
Oscillatory Characteristic ◽  
Piecewise Linear Transformation

Local oscillatory-characteristic decomposition (LOD) is a relatively new self-adaptive time-frequency analysis methodology. The method, based on local oscillatory characteristics of the signal itself uses three mathematical operations such as differential, coordinate domain transform, and piecewise linear transform to decompose the multi-component signal into a series of mono-oscillation components (MOCs), which is very suitable for processing multi-component signals. However, in the LOD method, the computational efficiency and real-time processing performance of the algorithm can be significantly improved by the use of piecewise linear transformation, but the MOC component lacks smoothness, resulting in distortion. In order to overcome the disadvantages mentioned above, the rational spline function that spline shape can be adjusted and controlled is introduced into the LOD method instead of the piecewise linear transformation, and the rational spline-local oscillatory-characteristic decomposition (RS-LOD) method is proposed in this paper. Based on the detailed illustration of the principle of RS-LOD method, the RS-LOD, LOD, and empirical mode decomposition (EMD) are compared and analyzed by simulation signals. The results show that the RS-LOD method can significantly improve the problem of poor smoothness of the MOC component in the original LOD method. Moreover, the RS-LOD method is applied to the fault feature extraction of rotating machinery for the multi-component modulation characteristics of rotating machinery fault vibration signals. The analysis results of the rolling bearing and fan gearbox fault vibration signals show that the RS-LOD method can effectively extract the fault feature of the rotating mechanical vibration signals.

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