In this paper, disks containing some or all zeros of a complex polynomial or eigenvalues of a complex matrix are developed. These disks are based on extensions of Cauchy classical bounds, Perron-Frobenius theory of positive matrices, and Gerschgorin theory. As a special case, given a real polynomial with real maximum or minimum zero, intervals containing the extreme zeros are developed. Moreover, methods for computing or refining these intervals are derived. Additionally, a closed form singular value decomposition of a characteristic polynomial was derived and utilized to compute new bounds for the zeros of polynomials. Finally, bounds which are based on zero transformation are given.
|Original language||English (US)|
|Number of pages||6|
|Journal||Proceedings of the American Control Conference|
|State||Published - Jan 1 2004|
|Event||Proceedings of the 2004 American Control Conference (AAC) - Boston, MA, United States|
Duration: Jun 30 2004 → Jul 2 2004