The Method of Steepest Descent and Automatic Solution of Polynomial Equations

摘要

The Morse-Kuiper Theorem is a recent improvement of what is known in the literature as the Morse Lemma which pertains to conditions under which a transformation of variables will reduce certain functions to quadratic forms. In this report a simplified proof is presented. A new method for automatic solution of polynomial equations is found independent of the method of steepest descent. A method is derived for accelerating the convergence of the sequence of approximations. The conditions for the J-test, to avoid the zeroes of the derivative, are improved. (Author)