Testing the sign-definiteness of forms

Summary (translated from the Russian): "To test the positive (nonnegative) definiteness of finite-dimensional quadratic forms and forms of the fourth degree we propose using classical methods of unconstrained optimization: the steepest descent method and the conjugate gradient method. Theoretical analysis and a computational experiment confirm the high efficiency of such an approach. The approach can be applied, in particular, to the problem of testing the sign-definiteness of an integral quadratic form in the calculus of variations."