Accession Number : AD0666971

Title :   USE OF THE IMPLICIT FUNCTION THEOREM IN SOLVING SYSTEMS OF EQUATIONS.

Descriptive Note : Research rept.,

Corporate Author : NAVY UNDERWATER SOUND LAB NEW LONDON CONN

Personal Author(s) : Goldstein,Marvin J.

Report Date : 02 FEB 1968

Pagination or Media Count : 25

Abstract : Applications of the implicit function theorem in solving systems of n equations in (n + p) unknowns subject to p nonlinear 'constraints' are discussed. A generalized iterative technique that is defined for a sufficiently restricted 'region' is derived for solving the set of (n + p) equations. The derivation employs Newton's method and assumes that the unconstrained (n + p) system of equations has a local vector function solution that satisfies the p constraints at a unique point in its 'prescribed region' of definition. The implicit function theorem is further employed to derive mathematical formulas that characterize the conditions of the solutions of systems of linear equations and the zeros of polynomials with real coefficients. (Author)

Descriptors :   (*EQUATIONS, PROBLEM SOLVING), DETERMINANTS(MATHEMATICS), CURVE FITTING, LINEAR SYSTEMS, NONLINEAR SYSTEMS, POLYNOMIALS, DIFFERENTIAL EQUATIONS, NUMERICAL METHODS AND PROCEDURES, SEQUENCES(MATHEMATICS), CONVERGENCE, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE