
Accession Number : AD0688942
Title : UPPER BOUNDS FOR THE ABSCISSA OF STABILITY OF A STABLE POLYNOMIAL.
Descriptive Note : Technical rept.,
Corporate Author : CALIFORNIA UNIV LOS ANGELES NUMERICAL ANALYSIS RESEARCH
Personal Author(s) : Henrici,Peter
Report Date : 1968
Pagination or Media Count : 13
Abstract : Let n be a positive integer, let a sub 1, a sub 2, ..., a sub n be real numbers, and let p be the polynomial p:z (arrow) z to the nth power + (a sub 1) z to the (n1) power +...+ a sub n. If the zeros of p are denoted by zeta sub 1, ..., zeta sub n, we call sigma: = max (1= or < i = or < n) Re (zeta sub i) the abscissa of stability of p. The polynomial p is called stable if and only if sigma < 0. Several lower bounds for the abscissa of stability have been given by G. F. Schrack. The purpose of this paper is to exhibit some negative upper bounds for the abscissa of stability of a polynomial that is already known to be stable. These bounds are elementary functions of the coefficients. (Author)
Descriptors : (*NUMERICAL ANALYSIS, POLYNOMIALS), (*POLYNOMIALS, STABILITY), DIFFERENTIAL EQUATIONS, INTEGRAL TRANSFORMS, COMPLEX VARIABLES, EXPONENTIAL FUNCTIONS, DETERMINANTS(MATHEMATICS), CONTROL SYSTEMS, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE