🚀 go-pugleaf

Suppose, I am dealing with the weighted least squares problem
y=A*x
(covariance matrix of y is C, weighting matrix W is inv(C))
and instead of using the ordinary
x=inv(A`*W*A)*A`*W*y
I use
x=inv(A`*W*A+alpha*E)*A`*W*y
where E denotes unit matrix and alpha is a parameter for
smoothing, stabilization, regularization or whatever you call it.
Sometimes it looks even useful in order not to bother with
singular matrices and pseudo inverses.

Now, my questions is, how do I get the covariance matrix of x
in this case? Is it equally simple as in the 1st case?

Thanks in advance for any helpful comment.

Chris

Christian Burger,
Dept. of Phys. Chemistry, U. of Marburg, Germany
e-mail: burger@dmrhrz11.bitnet