Evaluation of matrix element of a linear differential matrix equation by constrained least square fitting

5 views (last 30 days)
Hi All,
I was trying to evaluate the matrix coefficient by the method of constrained least square fitting. The linear matrix differential equation looks like X'=AX, where X' and X are two vectors and A is matrix. Moreover, there is a constraint on diagonal matrix element and which is a(i,i)=-Sum(i/=j)a(i,j). The elements of X' and X vectors are known. I was trying to use MATLAB to do that. But I didn't figure out which figure out which MATLAB function is suitable for that. Can you guide me in this regard.
Thanks in advance Sudipta

Accepted Answer

Richard Brown
Richard Brown on 7 Aug 2013
Assuming you have multiple X and X' vectors that you're trying to fit your matrix to, your problem can be posed as a constrained linear least squares problem in the entries of A, which can be solved using lsqlin
Richard Brown
Richard Brown on 7 Aug 2013
The vector that you get out from lsqlin will be the columns of A, stacked into a vector. The matrix Ahat that you provide to lsqlin will be big (it's not A). For example, assuming your vectors have m entries and A is square, the first m rows of the matrix Ahat you provide to lsqlin will be
tmp = repmat({x1},m,1);
Ahat(1:m,:) = blkdiag(tmp{:})
where x1 is your first X vector. Likewise the first m entries of the RHS will be xp1 (your first X' vector)

Sign in to comment.

More Answers (1)

Sudipta Sinha
Sudipta Sinha on 7 Aug 2013
Thanks for your reply. Yes, I have multiple x(1).....x(n) and x'(1).....x'(n) vectors. Can you provide a small script for that? That will be great for me.

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by