Otwarty dostęp

Probabilistic zero bounds of certain random polynomials


Zacytuj

A. Bloch and G. Pólya, “On the roots of certain algebraic equations,” Proc. London Math. Soc., vol. 33, pp. 102–114, 1932. Search in Google Scholar

A. T. Bharucha-Reid and M. Sambandham, Random Polynomials. Orlando, FL: Academic Press, 1986. Search in Google Scholar

J. E. Littlewood and A. C. Offord, “On the number of real roots of a random algebraic equation,” J. Lond. Math. Soc., vol. 13, pp. 288–295, 1938. Search in Google Scholar

J. M. Hammersley, “The zeroes of a random polynomial,” in Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Vol. II, Berkeley: University of California Press, 1956, pp. 89–111. Search in Google Scholar

M. Kac, “On the average number of real roots of a random algebraic equation,” Bull. Amer. Math. Soc., vol. 49, pp. 314–320, 1943. Search in Google Scholar

A. Bloch and G. Pólya, “On the roots of certain algebraic equations,” Proc. London Math. Soc., vol. 33, pp. 102–114, 1932. Search in Google Scholar

P. Erdős and P. Turán, “On the distribution of roots of polynomials,” Ann. of Math., vol. 51, no. 2, pp. 105–119, 1950. Search in Google Scholar

S. O. Rice, “The distribution of the maxima of a random curve,” Amer. J. Math., vol. 61, 1939, pp. 409–416. Search in Google Scholar

A. Edelman and E. Kostlan, “How many zeros of a random polynomial are real?,” Bull. Amer. Math. Soc., vol. 32, 1995, pp. 1–37. Search in Google Scholar

E. Kostlan, “On the distribution of roots of random polynomials,” in From Topology to Computation: Proceedings of the Smalefest, M. W. Hirsch, J. E. Marsden, and M. Shub, Eds. New York, NY: Springer-Verlag, 1993, pp. 419–431. Search in Google Scholar

L. A. Shepp and R. J. Vanderbei, “The complex zeros of random polynomials,” Trans. Amer. Math. Soc., 1995, pp. 4365–4384. Search in Google Scholar

V. Thangraj and M. Sambandham, “On Random Polynomials-II: A Survey,” Neural, Parallel, and Scientific Computations, vol. 29, no. 4, 2021, pp. 230–251. Search in Google Scholar

E. Dobriban and Z. Kabluchko, “On the distribution of complex roots of random polynomials with heavy-tailed coefficients,” SIAM Theory of Probability and its Applications, vol. 56, no. 4, 2011, pp. 537–571. Search in Google Scholar

Q. I. Rahman and G. Schmeisser, Analytic Theory of Polynomials: Critical Points, Zeros and Extremal Properties. London Mathematical Society Monographs, 2002. Search in Google Scholar

S. M. Ross, Introduction to Probability Models. Academic Press, 2014. Search in Google Scholar

W. Feller, An Introduction to Probability Theory and Its Applications. John Wiley & Sons, 2008. Search in Google Scholar

B. Datt and N. K. Govil, “On the location of the zeros of a polynomial,” J. Approx. Theory, vol. 24, 1978, pp. 78–82. Search in Google Scholar

B. Kalantari, “An infinite family of bounds on zeros of analytic functions and relationship to Smale’s bound,” Mathematics of Computation, vol. 74, 2005, pp. 841–852. Search in Google Scholar

M. Dehmer and A. Mowshowitz, “Bounds on the moduli of polynomial zeros,” Applied Mathematics and Computation, vol. 218, 2011, pp. 4128–4137. Search in Google Scholar

eISSN:
1339-0015
Język:
Angielski