Date: Wed, 25 Oct 2006 08:24:55
From: S Bond
Subject: Re: definiteness
Jonathan W. Ray wrote: > What is the easiest way to determine whether a matrix is positive definite? If the matrix is symmetric, try to compute the Cholesky factorization, it will only fail if the matrix is not positive definite. > What is the easiest way to determine whether a matrix is negative definite? Same as for positive definite, but with the negative of the matrix, i.e. let A = -B. Computing the Cholesky factorization, typically, requires fewer operations than computing all the eigenvalues. You can also find the "matrix inertia" which counts the number of positive, negative, and zero eigenvalues. Algorithms for computing this usually use the L D L^T factorization. See page 195 in the book, for example. This is basically the same amount of work as Choleksy.
|
HTML 4.01 Updated: Wed, 25 Oct 2006 08:24:55 | Powered by Perl Net::NNTP |