Sturm's Method in Counting Roots of Random Polynomial Equations

Efraim Shmerling () and Kenneth J. Hochberg ()
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Efraim Shmerling: College of Judea and Samaria
Kenneth J. Hochberg: Bar-Ilan University

Methodology and Computing in Applied Probability, 2004, vol. 6, issue 2, 203-218

Abstract: 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.

Keywords: random polynomial; Sturm's method (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:MCAP.0000017713.58934.d3

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