TY - JOUR

T1 - Sturm's method in counting roots of random polynomial equations

AU - Shmerling, Efraim

AU - Hochberg, Kenneth J.

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

KW - Random polynomial

KW - Sturm's method

UR - http://www.scopus.com/inward/record.url?scp=25844483318&partnerID=8YFLogxK

U2 - 10.1023/b:mcap.0000017713.58934.d3

DO - 10.1023/b:mcap.0000017713.58934.d3

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AN - SCOPUS:25844483318

SN - 1387-5841

VL - 6

SP - 203

EP - 218

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

IS - 2

ER -