MATLAB: An efficient Lagrange interpolation algorithm for multi-variate problems

interpolationlagrangepolynomials

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!

Best Answer

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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