Re: how to deal with the inversion problem of a huge sparse covariance matrix
- From: Rune Allnor <allnor@xxxxxxxxxxxx>
- Date: Sun, 27 Sep 2009 05:16:57 -0700 (PDT)
On 26 Sep, 20:16, "Hua Wang" <ehw...@xxxxxxx> wrote:
Dear All,
I am processing some data using weighted least-squares (WLS) method. As you know, the solution of a system function A*x=b with weighting matrix P is that: x=inv(A'*P*A)*(A'*P*b);
I am solving the system function using Cholesky decomposition. The formula is:
w=cholinc(P,'0');
x=(w*A)\(w*b);
I am not sure whether the above method is possible for the back slash operator. But first of all, I met the problem of calculating weight matrix P from the covariance matrix C, i.e. P=inv(C). It is almost impossible to get the inverse of the huge sparse matrix C.
Could anybody give me some suggestions to solve such equation A*x=B, giving huge sparse covariance matrix C? It is urgent for me!
I'm a bit curious what kinds of situations occur where you
need to handle a huge sparse covariance matrix.
First of all, most processes of practical interest are
stationary. You don't need the long-term covariances,
which means that you can get away with a smaller covariance
matrix.
Second, the cyclostationary processes that do have some
significant long-term covariance can be handled by specialized
higher-order techniques, so you don't need the *covariance*
matrix.
The remaining processes, that are not stationary or cyclo-
stationary, would require all the covariance data to be
available, so you would not use a *sparse* covariance matrix.
All in all, I think you might want to look over the problem
statement, to see if there are other approaches than the naive
go-straight-ahead-and-implement-the-literal-expressions.
That particular approach is almost always wrong.
Rune
.
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