century and has been referred to as Fourier's, Budan–Fourier, Fourier–Budan, and even Budan's theorem. Budan's original formulation is used in fast modern...

roots in (M(b), M(+∞)) */ if w = 0 then exit /* Budan's theorem */ if w = 1 then /* Budan's theorem again */ add (M(0), M(b)) to Isol if w > 1 then add...

method; Horner comments there and elsewhere on Budan's results, at first being sceptical of the value of Budan's work, but later warming to it. Thus, these...

existence of a root in an interval (Descartes' rule of signs, Sturm's theorem, Budan's theorem). They allow extending the bisection method into efficient algorithms...

count roots in any interval. This is the basic idea of Budan's theorem and the Budan–Fourier theorem. Repeated division of an interval in two results in...

there are other methods such as Descartes' rule of signs, Budan's theorem and Sturm's theorem for bounding or determining the number of roots in an interval...

1807, the French mathematician François Budan de Boislaurent generalized Descarte's result into Budan's theorem which counts the real roots in a half-open...

the Alesina–Galuzzi "a_b roots test" is Budan's "0_1 roots test". A detailed discussion of Vincent's theorem, its extension, the geometrical interpretation...

a list of things named after Joseph Fourier: Budan–Fourier theorem, see Budan's theorem Fourier's theorem Fourier–Motzkin elimination Fourier algebra Fourier...

S2CID 154334522. Akritas, Alkiviadis G. (1982). "Reflections on a pair of theorems by Budan and Fourier". Math. Mag. 55 (5): 292–298. doi:10.2307/2690097. JSTOR 2690097...

using Budan's theorem for separation of roots was given in 1842, by James R. Christie; it was noted by Young. In 1843 Young commented that Budan's approach...

Fourier's theorem on polynomial real roots, published in 1820. François Budan, in 1807 and 1811, had published independently his theorem (also known...