In a previous post, I mentioned that I have incorporated experiments in my Numerical Methods course. Here I will discuss the second experiment.
In this experiment, we find the length of two curves generated from the same points – one curve is a polynomial interpolant and another one is a spline interpolant.
Motivation behind the experiment: [...]
Posts Tagged as ‘Interpolation’
June 29, 2008
Length of a curve experiment
June 25, 2008
Shortest path for a robot
Imagine a robot that had to go from point to point consecutively (based on x values) on a two dimensional x-y plane. The shortest path in this case would simply be drawing linear splines thru consecutive data. What if the path is demanded to be smooth? Then what!
Well one may use polynomial or [...]
June 18, 2008
Finding the length of curve using MATLAB
As per integral calculus, the length of a continuous and differentiable curve f(x) from x=a to x=b is given by
S=
Now how do we find the length of a curve in MATLAB.
Let us do this via an example. Assume one asked you to find the length of from Π to 2Π. In the [...]
June 16, 2008
A simple MATLAB program to show that High order interpolation is a bad idea
In a previous post, we talked about that higher order interpolation is a bad idea.
In this post I am showing you a MATLAB program that will allow you to experiment by changing the number of data points you choose, that is, the value of n (see the input highlighted in red in the code – [...]
June 14, 2008
High order interpolation is a bad idea?
One would intuitively assume that if one was given 100 data points of data, it would be most accurate to interpolate the 100 data points to a 99th order polynomial. More the merrier: is that not the motto. But I am sorry to burst your bubble – high order interpolation is generally a [...]
June 10, 2008
If a polynomial of order n or less passes thru (n+1) points, it is unique!
Given n+1 (x,y) data pairs, with all x values being unique, then a polynomial of order n or less passes thru the (n+1) data points. How can we prove that this polynomial is unique?
I am going to show you the proof for a particular case and you can extend it to polynomials of any [...]
