ALGEBRAIC CHARACTERIZATION OF POLYNOMIALS WHOSE ZEROS LIE IN CERTAIN ALGEBRAIC DOMAINS

1 November 1969

journal article
Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences

Vol. 64 (3) , 818-823
https://doi.org/10.1073/pnas.64.3.818

Abstract

A new algebraic criterion is given for a polynomial φ with complex coefficients to have all its zeros in a certain type of algebraic region T of the complex plane. In particular, T may be any circle or half plane. The criterion is effectively computable from the coefficients of the polynomial φ. The classical results of Hermite, Hurwitz, Lyapunov, Schur-Cohn, and others appear as special cases of the new criterion.

Keywords

POLYNOMIAL
ZEROS LIE
ALGEBRAIC CRITERION
SPECIAL CASES
ALGEBRAIC REGION
ALGEBRAIC DOMAINS
COMPLEX COEFFICIENTS
SCHUR COHN
COMPLEX PLANE

This publication has 0 references indexed in Scilit: