Re: Regularized lsqr

On Jul 7, 11:42 pm, John D'Errico <woodch...@xxxxxxxxxxxxxxxx> wrote:
In article <1183810770.617462.171...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, fas <faisalmu...@xxxxxxxxx> wrote:
Hi
I am sorry I made a mistake, here is the correct version

Sum_k [ || A_k *x - b_k || ] + Sum_k[w* (x'A_k' A_k x)] + lambda^2 ||
L*x ||

we have k copies of A (matrices) and b(vectors) but not only one copy
of 'L' operator. So I have transformed all A_k as A (stacked copies of
A_k) and same goes for b_k. Then I think we can write it as,

No. You still cannot minimize a sum of norms
using lsqr. You can only minimize a sum of
squares of those norms.

John

--
The best material model of a cat is another, or preferably the same, cat.
A. Rosenblueth, Philosophy of Science, 1945

Those who can't laugh at themselves leave the job to others.
Anonymous

I am once again sorry for the typing mistake, I indeed mean norm-2 so
||.|| stand for ||.||^2 .
Therefore the equation that I am trying to minimize is

|| A*x - b ||^2 + w* || A*x ||^2 + lambda^2 || L*x ||^2
However my concern is the dimensions for 1,2 and the third terms, as I
mentioned earlier that A is a sum of k matrices while L is a single
matrix and I would like to know if it can be minimized jointly.
Thanks again for your patience in your replies.

.

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