On the Optimum Criterion of Polynomial Stability |
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Authors: | XIE, LANG XIE, LIN |
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Affiliation: | Mathematics Department, Liaoning Normal University Dalian City, Liaoning Province, People's Republic of China |
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Abstract: | The purpose of this note is to answer the question raised byNie & Xie (1987). Let f(x)=a0xn+a1xn1+...+an be apositive-coefficient polynomial. The numbers 1=ai-1ai+2/aiai+1(i=1, ..., n2) are called determining coefficients. Theoptimum criterion problem was posed as follows: for n3, findthe maximal number (n) such that the polynomial f(x) is stableif i < (n) (1in2). For n6, we show that (n)=ß,where ß is the unique real root of the equation x(x+1)2=1. |
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