Trouble with interpolation and gridding data points

suppose i have plane which is a subset of and i consider certain intervals on and i want to grid this in both , with some step size say and interpolate for all using the grid points, and i have a known function, where values of and are known.

The interpolation i want to use is and find the error

How would i grid the x1-x2 plane ? and how to use the interpolation formula there ? Any help ?

Answer 1

[dpb]

Write a (vectorized) function for M(x1,x2), compute the interpolating grid [X,Y] with meshgrid and then call the function with [X,Y]

Not clear to me, however, where x2 enters into M, though, altho the text is so small I can't really read it.

[Siddhartha Ganguly]

Hey thanks for the answer. Could you expand your answer a bit more, how do i write the vectorized function and meshgrid, i'm new to matlab. Which part you're having trouble to read ?

[Image Analyst]

D1 = -100;
D2 = 100;
X = D1 : 0.01 : D2;
Y = D1 : 0.01 : D2;
[x1, x2] = meshgrid(X, Y);
phi = k1*x1 + k2*x2;
imshow(phi, []);

Note, there are far too many points to see on your screen without zooming way in, but you can look at phi in the workspace variable inspector if you want.

[Siddhartha Ganguly]

Thanks for the reply, how do find ? this will take two inputs right, both x1 and x2 , in the above formula for argument of phi is a vector and , then may be i'll have

, How do i write this vector sum and use the interpolation ?

[Siddhartha Ganguly]

@Image Analyst @dpb any idea on the interpolation and the sum, how do i proceed with this ?