Accession Number : AD0819800

Title :   THE METHOD OF STEEPEST DESCENT AND AUTOMATIC SOLUTION OF POLYNOMIAL EQUATIONS.

Descriptive Note : Final technical rept. 1 Mar 66-30 Jun 67,

Corporate Author : BASEL UNIV (SWITZERLAND) MATHEMATICS INST

Personal Author(s) : Ostrowski, Alexander M.

Report Date : AUG 1967

Pagination or Media Count : 10

Abstract : The Morse-Kuiper Theorem is a recent improvement of what is known in the literature as the Norse 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 aviod the zeroes of the derivative, are improved.

Descriptors :   *POLYNOMIALS), (*EQUATIONS, NUMERICAL ANALYSIS, APPROXIMATION(MATHEMATICS), EQUATIONS, TRANSFORMATIONS(MATHEMATICS), SEQUENCES(MATHEMATICS), CONVERGENCE, FUNCTIONS(MATHEMATICS).

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE