What kind of Interpolation Algorithm Will be Applicable for the Following data set to obtain smooth curve?

Hello there,

I have a following data set,

x =     
[443.0000  443.9000  482.0000  496.6000  560.0000  561.4000  654.6000  664.5000  703.9000  740.2000  782.5000  835.1000  864.7000  864.8000  1608.9000  1613.7000  2200.7000  2202.4 ]
y =     
[1.0464  1.0641  0.9832  0.9631  0.9370  0.9358  0.9611  0.9574  0.9820  0.9955  1.0287  1.0034  1.0021  1.0063  1.0372  1.0336  1.0343  1.0290 ]

This plot represents the actual data set

Now I was doing shape preserving interpolation

In this case, this type of interpolation following the actual data, At this point I want to perform different interpolation algorithm which helps to smoothing the interpolating data set.

Could you please share any idea?

Thank you.

[John D'Errico]

If the algorithm changes the data (i.e., smooths it) then it is not interpolation.

Answer 1

[Bruno Luong]

It looks like your data has a couples of pairs/tripples that are closely spread.

I suggest to merge thme to a single point then fit the data that are merged.

x =      [443.0000  443.9000  482.0000  496.6000  560.0000  561.4000  654.6000  664.5000  703.9000  740.2000  782.5000  835.1000  864.7000  864.8000  1608.9000  1613.7000  2200.7000  2202.4 ];
y =    [1.0464  1.0641  0.9832  0.9631  0.9370  0.9358  0.9611  0.9574  0.9820  0.9955  1.0287  1.0034  1.0021  1.0063  1.0372  1.0336  1.0343  1.0290 ];

[xu,~,J]=uniquetol(x,10,'DataScale',1);
xi=linspace(min(x),max(x),500);
yu=accumarray(J(:),y(:),[],@mean);
yi=interp1(xu,yu,xi,'makima');

plot(x,y,'or',xi,yi,'b');

[suraj karki]

Appriciated Burno

[Bruno Luong]

You are welcome

PS: I just edit the code to take the average of y before interpolation.

[suraj karki]

The second Graphs shows more physical meaning. Thank a lot Burno