I used least square method but matlab return compeletly wrong answer

Question

I must solve an over constrained problem (Equations more than unknowns). So I have to use least square method. First I create coefficient matrix .It is a 225*375 matrix. For inversing, I use pinv() function and then multiply it in load matrix . My problem is about plate bending under uniform load with clamped edge. I expect at least correct answer in my boundary (the deflection must be zero), but even in boundary I have wrong answer. I have read in a book that sometimes an error occurs in the Least Square method, which should be corrected manually by the user but I couldn't find any more explanation about it elsewhere.

Answer 1

First of all we need more data about your problem:

1. What's the model?
2. Where are the measurements coming from?

Yet few notes about what I could figure from your issue:

1. If you have boundaries on the solution you should use Constrained Least Squares. If you do it on MATLAB it is easily can be done (Look at Quadratic Programming as well).
2. Does L2 error fit your problem? Maybe you should a different
3. There's no bug in the implementation of MATLAB. Using pinv gives the minimum norm (Both of the solution vector and the residual L2 norm) solution in the range of the given matrix. It might be you either construct the data in a wrong manner or the model you're using isn't adequate.