THE TEACHING OF MATHEMATICS

THE TEACHING OF MATHEMATICS
Cauchy-type inclusion and exclusion regions for polynomial zeros
Aaron Melman

Abstract

A classical result by Cauchy defines a disk containg all the zeros of a polynomial. We derive several related results by using similarity transformations of a polynomial's companion matrix, together with Gershgorin's theorem. We thus show that Cauchy's original result can be seen as but one member of a family of related results.

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Keywords: Cauchy; Gershgorin; zero location; root location; polynomial.

Pages:  39$-$50     

Volume  XVII ,  Issue  1 ,  2014