An efficient Lagrange interpolation algorithm for multi-variate problems

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Xiaohan Du
Xiaohan Du 2016-11-28
回答： Vishal Neelagiri 2016-12-6
Hi all,
I'd like to perform a multi-variate Lagrange interpolation for matrices. Here is a simple example:
Imagine there are 4 points in a Cartesian coordinate system:
coord = [1 1; 1 2; 2 1; 2 2];
and related four 2 by 2 matrices:
samp_1 = [1 2; 3 4];
samp_2 = [2 3; 4 5];
samp_3 = [1 3; 5 7];
samp_4 = [2 4; 6 8];
Therefore applying Lagrange polynomials, the result of interpolation at point [1.5, 1.5] is
otpt = [1.5 3; 4.5 6];
Similarly, the results at point [1.8, 1.3] is
otpt = [1.3 3.1; 4.9; 6.7];
Is there a code in MATLAB to achieve this (for any size of matrices)? I have my own solution but it is not very efficient, and it needs to perform matrix inverse, which takes time. I'd like to hear your ideas.
Many thanks!

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Vishal Neelagiri
Vishal Neelagiri 2016-12-6
You might find the following File Exchange submission and the MATLAB Answers page helpful regarding this:
http://www.mathworks.com/matlabcentral/fileexchange/899-lagrange-polynomial-interpolation
https://www.mathworks.com/matlabcentral/answers/3338-lagrange-interpolation-m

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