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 > E-mail: [EMAIL PROTECTED] > Tel: 212-772-5308 > Fax: 212-772-4858 > > ______________________________________________ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html -- Spencer Graves, PhD Senior Development Engineer PDF Solutions, Inc. 333 West San Carlos Street Suite 700 San Jose, CA 95110, USA [EMAIL PROTECTED] www.pdf.com <http://www.pdf.com> Tel: 408-938-4420 Fax: 408-280-7915 ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html