Sturm's Method in Counting Roots of Random Polynomial Equations |
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Authors: | Shmerling Efraim Hochberg Kenneth J |
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Institution: | (1) Department of Mathematics, College of Judea and Samaria, 44837 Ariel, Israel;(2) Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel |
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Abstract: | The problem of finding the probability distribution of the number of zeros in some real interval of a random polynomial whose coefficients have a given continuous joint density function is considered. An algorithm which enables one to express this probability as a multiple integral is presented. Formulas for the number of zeros of random quadratic polynomials and random polynomials of higher order, some coefficients of which are non-random and equal to zero, are derived via use of the algorithm. Finally, the applicability of these formulas in numerical calculations is illustrated. |
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Keywords: | random polynomial Sturm's method |
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