[R] Efficient testing for +ve definiteness

Spencer Graves spencer.graves at pdf.com
Thu Jul 14 05:22:48 CEST 2005

	  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 

	  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
> E-mail: makram.talih at hunter.cuny.edu
> Tel: 212-772-5308
> Fax: 212-772-4858
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Spencer Graves, PhD
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