Checking the definiteness of forms

It is suggested to verify the positive definiteness (or semidefiniteness) of finite quadratic and fourth-degree forms on the basis of the classical unconstrained optimization techniques, such as the steepest descent method and the conjugate gradient method. A theoretical analysis and computational experiments confirm the efficiency of this approach. In particular, it is applied to verifying the definiteness of an integral quadratic form that occurs in the calculus of variations. Copyright © 2002 by MAIK "Nauka/Interperiodica ".