UPPER BOUNDS FOR THE ABSCISSA OF STABILITY OF A STABLE POLYNOMIAL.
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 (n-1) 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1968
- Accession Number
- AD0688942
Entities
People
- Peter Henrici
Organizations
- University of California, Los Angeles