Determining the number of real roots of polynomials through neural networks
نویسندگان
چکیده
منابع مشابه
Determining the number of real roots of polynomials through neural networks
The ability of feedforward neural networks to identify the number of real roots of univariate polynomials is investigated. Furthermore, their ability to determine whether a system of multivariate polynomial equations has real solutions is examined on a problem of determining the structure of a molecule. The obtained experimental results indicate that neural networks are capable of performing th...
متن کاملReal Roots of Polynomials through Neural Networks
K e y w o r d s R o o t s of polynomials, Neural networks, Number of zeros. 1. I N T R O D U C T I O N Numerous problems in mathemat ical physics, robotics, computer vision, computa t ional geometry, signal processing etc., involve the solution of polynomial systems of equations. Recently, artificial feedforward neural networks (FNNs) have been applied to the problem of comput ing the roots of ...
متن کاملComputing the Number of Real Roots of Polynomials through Neural Networks
Numerous problems in robotics, computer vision, computational geometry and signal processing, involve the solution of polynomial systems of equations. Recently, Artificial Feedforward Neural Networks (FNNs) have been applied to perform the factorization of polynomials [4, 5, 6] with considerable success. To the best of our knowledge the problem of computing the number of real roots of a polynom...
متن کاملOn the Number of Real Roots of Random Polynomials
Roots of random polynomials have been studied exclusively in both analysis and probability for a long time. A famous result by Ibragimov and Maslova, generalizing earlier fundamental works of Kac and Erdős-Offord, showed that the expectation of the number of real roots is 2 π logn + o(logn). In this paper, we determine the true nature of the error term by showing that the expectation equals 2 π...
متن کاملOn the Number of Real Roots of Polynomials
Our main theorem, proved in § 2 establishes some of the properties of F(x, y) = 0 when we drop all restrictions on / and require only that all the roots of h be real (of arbitrary sign). In the last section, we apply this theorem to obtain an extension of Theorem 1.1 which states that, for h restricted as in Pόlya's theorem, there are at least as many intersection points as the number of real r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2006
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2005.07.012