Stability of the roots of random algebraic polynomials |
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Authors: | Mark J Christensen A T Bharucha-Reid |
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Institution: | 1. School of Mathematics , Georgia Institute of Technology , Atlanta, Georgia, 30332;2. Department of Mathematics , Wayne State University , Detroit, Michigan, 48202 |
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Abstract: | In this paper we consider the behavior of the roots of random algebraic polynomials. A code was developed which generates a sample of random algebraic polynomials, calculates the roots of each sample polynomial, and then calculates the averages of the roots. Finally, the roots of the deterministic algebraic polynomial whose coefficients are the averages of the sample coefficients are calculated. These data are then tabulated and graphically displayed. The relationship between the averages of the roots of the sample polynomials and the roots of the average polynomial is discussed. |
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Keywords: | random algebraic polynomial polydisk analytic functions computer simulation |
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