Q: solving ax=0 with regularization?

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Elvis Chen
Elvis Chen il 5 Mar 2012
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,

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Risposte (1)

Andrew Newell
Andrew Newell il 5 Mar 2012
There is a package called regtools in the File Exchange that might help.
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Andrew Newell
Andrew Newell il 6 Mar 2012
Why do you want to do it that way? I don't see any advantage.
Elvis Chen
Elvis Chen il 7 Mar 2012
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,

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