At 03:46 PM 7/6/00 +0000, Christian A. Walter wrote:
>Does anyone know if there is a structured way to adjust a negative
>definite matrix such that it becomes semi-definite, while "minimizing"
>the induced changes to the matrix?
>
>Cheers,
>Christian
I posed a similar question to edstat last fall. I was specifically
concerned with non-positive-definite correlations matrices. Several people
suggested to me the following numerical solution: get the eigenvectors and
eigenvalues, set the negative eigenvalues to zero (there's generally only
one that's negative) and proportionately adjust the others to maintain the
same sum (total variance), and reconstruct the correlation matrix. This
seems to work very well in practice. I've also done some simulations,
beginning with a well-conditioned correlation matrix and gradually changing
it until it becomes slightly ill-conditioned. The eigen procedure
successfully 'corrects' the matrix.
Rich Strauss
========================
Dr Richard E Strauss
Biological Sciences
Texas Tech University
Lubbock TX 79409-3131
Email: [EMAIL PROTECTED]
Phone: 806-742-2719
Fax: 806-742-2963
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