Hello Dear, mostly we use cubic spline more than Lagrange in interpolation because spline gives good approximate more than Lagrange .. I want to ask what exactly advantage for spline and Lagrange .. and can I compare between us by smoothness? and when Lagrange became better than cubic spline?
I mean, I need to know how much cubic spline smooth because its content many splines and already give us piecewise function, actually, this is the advantage of spline .. but what about Lagrange ? and how can I compare between them?
Thank you in advance
In term of accuracy (relatively error or MAPE) and memory (related to my field), yes spline is better because of piecewise point. To improvise your Lagrange scheme, simple solution is by segmented the approximation into smaller segment or use an improvise Lagrange (trisection) with additional d as an offset either you varies upward or downward, thus reduce the error of normal Lagrange.
Dear,
LAGRANGE polynomial is not suitable to interpolate the experimental data. Thus, the spline interpolation as an alternative approach. Especially, the common cubic spline leads to a smooth interpolation.
Regards
Dear Dr. Ali,
Why Lagrange not suitable and why cubic spline suitable .. actually that is my question.
Thank you very much for your feedback.
Dear Dr. Muhammad Sufyan Safwan Mohamad Basir,
thank you very much for your feedback.
Dear Mustafa,
Based upon a given set of
experimental data ( 11 experiment)
LAGRANGE interpolation polynom of degree ten. Because of its oscillation property the LAGRANGE polynomial is not suitable to interpolate the given experimental data. Thus, the spline interpolation has been discused as an alternative approach. Especially, the common cubic spline leads to a smooth interpolation.
Furthermore, it has been illustrated that high-degree splines are approaching to LAGRANGE polynomials. A spline of degree = infinity is identical to the LAGRANGE approximation.
Regards
First one might ask how well one must interpolate to solve the problem at hand?
If there is no error and an underling physical process, use the underling physical process to set up a model for the data to be interpolated.
Fit the model to the data and interpolate applying the model.
If there is error in the data, what do you know about the error?
Are there ways to minimizing the error in interpolation? What are they?
Will any provide the accuracy needed for the problem at hand?
If you do not know the underlying physical process, why not use linear interpolation between closest pairs of data points?
The questions I provide here are meant for discussion; questions for the reader or others to answer.
Prof. @Jack Kornfield
Actually, I asking about which one of them better In other respects, I didn't ask about accuracy. I mean I was asking about smoothing and other advantages for them.
thank you very much for your feedback
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