Re: [R] Efficient testing for +ve definiteness

From: Spencer Graves <spencer.graves_at_pdf.com>
Date: Thu 14 Jul 2005 - 13:22:48 EST

          My preference is to test see if the smallest eigenvalue is less than something like sqrt(.Machine$double.eps) times the largest. This may be too conservative, but if the ratio of the smallest to the largest is less than some small number like that, the inverse of such a real symmetric matrix will have very large eigenvalue(s) in potentially unstable directions. R may have other functions beside eigen that will explicitly consider the symmetry of a matrix, but I'm not familiar with them.

          spencer graves

Makram Talih wrote:

> Dear R-users,
>
> Is there a preferred method for testing whether a real symmetric matrix is
> positive definite? [modulo machine rounding errors.]
>
> The obvious way of computing eigenvalues via "E <- eigen(A, symmetric=T,
> only.values=T)$values" and returning the result of "!any(E <= 0)" seems
> less efficient than going through the LU decomposition invoked in
> "determinant.matrix(A)" and checking the sign and (log) modulus of the
> determinant.
>
> I suppose this has to do with the underlying C routines. Any thoughts or
> anecdotes?
>
> Many Thanks,
>
> Makram Talih
>
> --
> Makram Talih, Ph.D.
> Assistant Professor
> Department of Mathematics and Statistics
> Hunter College of the City University of New York
> 695 Park Avenue, Room 905 HE
> New York, NY 10021
>
> Website: http://stat.hunter.cuny.edu/talih
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> Fax: 212-772-4858
>
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Received on Thu Jul 14 13:28:19 2005

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