A Proof of Brace's Theorem by Induction.
Abstract
Grace's theorem states: Let the polynomials be apolar. If the circular region C contains all the zeros of A(z), then C must contain at least one of the zeros of B(z). By a circular region is meant either the closed interior of a circle, or the closed exterior of a circle, or a closed half-plane. This document gives a proof of Grace's theorem by mathematical induction on the degree n. Keywords: Zeros of polynomials; Mobius transformations.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1985
- Accession Number
- ADA163714
Entities
People
- A. W. Goodman
- Isaac Jacob Schoenberg
Organizations
- University of Wisconsin–Madison