Stability and Oscillation Regions of Polynomials

• Main Authors: Shih Shan Chiou, 邱士珊
• Other Authors: Sui Sun Cheng
• Format: Others
• Language: en_US
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/77146186153070765658

碩士 === 國立清華大學 === 數學系 === 93 === ABSTRACT In this thesis, we are concerned with the stability and oscillation regions of polynomials. In Section 2, given an arbitrary real quartic polynomial, we find the exact region containing the coefficients of the polynomial such that all roots have absolute value less than 1. In Section 3, given an arbitrary real quintic polynomial, we are concerned with the necessary and suf- ficient conditions imposed on the parameters of the polynomial so that all its roots are non-positive. By means of the method of envelopes, we are able to derive the exact region containing these parameters.