Find values of two variables corresponding to query points of two matrices.

If Ithere are 2 equations A(x,y) and B(x,y) that are functions of 2 varibles x, y. Suppose I set some values for x and y as vectors with lenghts i and k, respectively. Then I calclauted the matrices A (ixk) and B(ixk) corresponding to x, and y vectors.

How can I determine x, and y values for which A(x,y) and B(x,y) equal certain values (say v1 and v2) that are not in the calculaetd matrices?!

I think I should use "interpolation" but I don't know how I can apply it for this case.

Answer 1

[Matt J]

You should use fsolve or fminsearch to solve the original equations. Both of these are iterative solvers requiring an initial guess (x0,y0) of the solution.The matrices A and B can be used to do a discrete search for an approximate solution, which can serve as your (x0,y0):

[~,jmin]=min(hypot(A-v1,B-v2),[],'all','linear');

[x0,y0]=ind2sub([i,k], jmin);

x0=xvector(x0); y0=yvector(y0); %initial guess