Testing the definiteness of matrices on polyhedral cones (Q1104045)

The author gives finite criteria for determining whether a real symmetric matrix is nonnegative definite, nonnegative definite plus, or positive definite on a convex polyhedral cone using the principal pivoting scheme for quadratic programming. Moreover, if a criterion gives an indication that a real symmetric matrix does not belong to a certain conditional definiteness class, the author shows how to determine a point in the polyhedral cone in which the definiteness class in question is violated. A procedure and some numerical examples are also given.