Q: solving ax=0 with regularization?

hi all,

I would like to solve a system of equations of the following form:

A_{nx9} X_{9x1} = 0_{nx1}

Where A is a matrix (known) obtained from a set of observation, and X (unknown) is a vector derived from some state variables. In fact, X is the Kronecker project of 2 unit vectors:

X = kron( a_{1x3},b_{1x3} )'

where |a| = |b| = 1.

Since A is constructed from a set of observations, each rows are not exactly independent of each other. In general, n>>9, and if I attempt to solve X by solving the null-space, I end up with basis functions that satisfies the equation, but not a particular solution.

From my limited knowledge of linear algebra (still reading upon it), I understand AX=0 could be solve using some iterative solver with regularization. My question is:

How can I solve AX=0 in matlab while using |a| = |b| =1 as a regularization term?

any help is very much appreciated,

Answer 1

[Andrew Newell]

There is a package called regtools in the File Exchange that might help.

[Elvis Chen]

hi,

First of, thanks for the reply. As my understanding on this subject is limited, what I'm not clear of is the following.

Most of the regularization terms involves the state vector itself, i.e. the X in AX=0. In my case, X is the kronecker product of 2 vectors a, and b, and it is the vectors a and b I want to use as regularization term instead.

thus, is there anyway to do this?

[Andrew Newell]

Why do you want to do it that way? I don't see any advantage.

[Elvis Chen]

this is how the system of equations were formulated. I'm trying to re-formulate it to see if I can use the vectors a and b directly, but I doubt it.

thanks,