In mathematics, Budan's theorem is a theorem for bounding the number of real roots of a polynomial in an interval, and computing the parity of this number.

The Budan-Fourier Theorem gives an upper bound on the number of real roots (counting multiplicity) of a real polynomial in a given interval I = ( a , b ] , ...

24 апр. 2012 г. · An application of the statement of (only) Budan's theorem in computer algebra may be found in [Ak3], where it is used as a no roots test.

14 нояб. 2017 г. · Budan's theorem gives an upper bound for the number of real roots of a real polynomial in a given interval (a,b). This bound is not sharp (see ...

In elementary text-books the theorem is sometimes stated in a simplified form obtained by imposing the condition that neither f(a) nor f(b) is zero. It is a ...

Budan's theorem. (mathematics) A theorem for bounding the number of real roots of a polynomial in an interval, and computing the parity of this number.

2 сент. 2018 г. · When all roots are known to be real, the over-approximation becomes tight: we can utilise this theorem to count real roots exactly. It is also ...

27 июн. 2013 г. · In chapter 1 we present the historical proof of Budan's theorem, define virtual roots and explain some of their properties. This should be ...

21 мар. 2017 г. · is a non-negative even integer. Thus the Budan–Fourier theorem states that the number of roots in the interval is equal to. V(a)-V(b).

26 мая 2024 г. · When all roots are known to be real, the over-approximation becomes tight: we can utilise this theorem to count real roots exactly. It is also ...