Creating huge fourier matrix
1 view (last 30 days)
Show older comments
I need to minimize |FT^-1(Ax-B)| using lsqr. A is a huge matrix which I had to define using spalloc. Since fft() can't handle sparse matrix, I'm trying to perform the fourier transform via multiplication with fourier matrix
F=dftmtx(N)
in order to compute
x=lsqr(F*A,fft(B))
However, N is too large so I can't create F. Is there any method to handle large fourier matrix? Thank you for the help.
0 Comments
Answers (1)
Matt J
on 30 Dec 2015
Edited: Matt J
on 30 Dec 2015
Note that | | FT^-1(Ax-B) | | = | | Ax-B | |. This can be seen from Parseval's theorem, or just from basic properties of orthogonal matrices. In other words, you can equivalently just do lsqr(A,B) or A\B and there is no need to actually implement the FT operator at all.
Note also that lsqr(P,Q) does not require that P be a matrix. In the documentation for lsqr, you will see that it can also be a function handle to a function that implements the operations P*x and P' * x.
3 Comments
Christine Tobler
on 31 Dec 2015
You could take a look at example 2 in the lsqr documentation for how to define a function handle input to lsqr.
See Also
Categories
Find more on Geology in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!