Asymptotic variance of the number of real roots of random polynomial systems

D. Armentano; J-M. Azaïs; F. Dalmao; J. R. León

doi:10.1090/proc/14215

Asymptotic variance of the number of real roots of random polynomial systems

Proceedings of the American Mathematical Society ◽

10.1090/proc/14215 ◽

2018 ◽

Vol 146 (12) ◽

pp. 5437-5449 ◽

Cited By ~ 1

Author(s):

D. Armentano ◽

J-M. Azaïs ◽

F. Dalmao ◽

J. R. León

Keyword(s):

Asymptotic Variance ◽

Polynomial Systems ◽

Random Polynomial ◽

Real Roots ◽

Number Of Real Roots

Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems

American Journal of Mathematics ◽

10.1353/ajm.2021.0026 ◽

2021 ◽

Vol 143 (4) ◽

pp. 1011-1042

Author(s):

D. Armentano ◽

J-M. Azaïs ◽

F. Dalmao ◽

J. R. León

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Polynomial Systems ◽

Random Polynomial ◽

Real Roots ◽

Number Of Real Roots

ON THE EXPECTED NUMBER OF REAL ROOTS OF A SYSTEM OF RANDOM POLYNOMIAL EQUATIONS

Foundations of Computational Mathematics ◽

10.1142/9789812778031_0007 ◽

2002 ◽

Cited By ~ 9

Author(s):

ERIC KOSTLAN

Keyword(s):

Polynomial Equations ◽

Random Polynomial ◽

Expected Number ◽

Real Roots ◽

Number Of Real Roots

What is the Least Expected Number of Real Roots of a Random Polynomial?

Theory of Probability and Its Applications ◽

10.1137/s0040585x97983389 ◽

2009 ◽

Vol 53 (1) ◽

pp. 117-133 ◽

Cited By ~ 2

Author(s):

A. Nazarov ◽

D. Zaporozhets

Keyword(s):

Random Polynomial ◽

Expected Number ◽

Real Roots ◽

Number Of Real Roots

On the Lower Bound for the Number of Real Roots of a Random Algebraic Equation

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/2007/74191 ◽

2007 ◽

Vol 2007 ◽

pp. 1-8

Author(s):

Takashi Uno

Keyword(s):

Lower Bound ◽

Algebraic Equation ◽

Random Variables ◽

Real Roots ◽

Number Of Real Roots

We estimate a lower bound for the number of real roots of a random alegebraic equation whose random coeffcients are dependent normal random variables.

On the variance of the number of real roots of random algebraic polynomials

Stochastic Analysis and Applications ◽

10.1080/07362998308809013 ◽

1983 ◽

Vol 1 (2) ◽

pp. 215-238 ◽

Cited By ~ 2

Author(s):

M. Sambandham ◽

V. Thangaraj ◽

A.T. Bharucha-Reid

Keyword(s):

Algebraic Polynomials ◽

Real Roots ◽

Random Algebraic Polynomials ◽

Number Of Real Roots

ON THE NUMBER OF REAL ROOTS OF A QUINTIC EQUATION: ADDENDUM

The Quarterly Journal of Mathematics ◽

10.1093/qmath/os-5.1.240 ◽

1934 ◽

Vol os-5 (1) ◽

pp. 240-240

Author(s):

T. W. CHAUNDY

Keyword(s):

Real Roots ◽

Quintic Equation ◽

Number Of Real Roots

Two theorems on the number of real roots of the characteristic equation of any stable linear physical system

Transactions of the American Institute of Electrical Engineers Part II Applications and Industry ◽

10.1109/tai.1959.6371518 ◽

1959 ◽

Vol 77 (6) ◽

pp. 670-673

Author(s):

J. F. Koenig

Keyword(s):

Characteristic Equation ◽

Physical System ◽

Real Roots ◽

Number Of Real Roots ◽

Stable Linear

On the lower bound of the number of real roots of a random algebraic equation with infinite variance. III

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1973-0315786-8 ◽

1973 ◽

Vol 39 (1) ◽

pp. 184-184 ◽

Cited By ~ 2

Author(s):

G. Samal ◽

M. N. Mishra

Keyword(s):

Lower Bound ◽

Algebraic Equation ◽

Infinite Variance ◽

Real Roots ◽

Number Of Real Roots

ON THE NUMBER OF REAL ROOTS OF A QUINTIC EQUATION

The Quarterly Journal of Mathematics ◽

10.1093/qmath/os-5.1.10 ◽

1934 ◽

Vol os-5 (1) ◽

pp. 10-22

Author(s):

T. W. CHAUNDY

Keyword(s):

Real Roots ◽

Quintic Equation ◽

Number Of Real Roots

A note about the average number of real roots of a Bernstein polynomial system

Journal of Complexity ◽

10.1016/j.jco.2009.03.001 ◽

2009 ◽

Vol 25 (4) ◽

pp. 339-342 ◽

Cited By ~ 2

Author(s):

Diego Armentano ◽

Jean-Pierre Dedieu

Keyword(s):

Bernstein Polynomial ◽

Polynomial System ◽

Real Roots ◽

Number Of Real Roots