An asymptotic expansion for the expected number of real zeros of a random polynomial
Author:
J. Ernest Wilkins
Journal:
Proc. Amer. Math. Soc. 103 (1988), 12491258
MSC:
Primary 60G99
MathSciNet review:
955018
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Abstract: Let be the expected number of real zeros of a polynomial of degree whose coefficients are independent random variables, normally distributed with mean 0 and variance 1. We find an asymptotic expansion for of the form in which . The numerical values of calculated from this expansion, using only the first four, or six, coefficients, agree with previously tabulated seven decimal place values with an error of at most when , or .
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 Y. J. Wang, Bounds on the average number of real roots of a random algebraic equation, Chinese Ann. Math. Ser. A. 4 (1983), 601605. MR 742181 (85c:60081)
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 J. E. Wilkins, Jr., An upper bound for the expected number of real zeros of a random polynomial, J. Math. Anal. Appl. 42 (1973), 569577. MR 0326842 (48:5184)
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 Z. H. Luo, The average number of real roots of a random algebraic equation, Chinese Ann. Math. 1 (1980), 541544. MR 619600 (83b:10067)
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 M. J. Christensen and M. Sambandham, An improved lower bound for the expected number of real zeros of a random polynomial, Stochastic Anal. Appl. 2 (1984), 431436. MR 769280 (86e:60044)
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 Z. M. Yu, Bounds on the average number of real roots for a class of random algebraic equations, J. Math. Res. Exposition 2 (1982), 8185. MR 669828 (84h:60081)
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 D. K. Kahaner, Some computations of expected number of real zeros of random polynomials, J. Math. Anal. Appl. 48 (1974), 780784. MR 0418402 (54:6443)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198809550181
PII:
S 00029939(1988)09550181
Article copyright:
© Copyright 1988
American Mathematical Society
