Vandermonde determinant

Vandermonde determinant

[′van·dər‚mōnd di‚tər·mə·nənt]
(mathematics)
The determinant of the n × n matrix whose i th row appears as 1, xi , xi 2,…, xi n-1where the xi k appear as variables in a given polynomial equation; this provides information about the roots.
References in periodicals archive ?
Moreover, in the case of alternants related to the inverse scattering problem this quotient equals unity, i.e., the alternant itself equals the Vandermonde determinant. These useful properties of alternants are the key to a very simple final result expressed by Eq.
The CAA-group has developed MATLAB software to compute such nearly optimal points for several geometries, e.g., the disk and the simplex, not only for minimizing the Lebesgue constant but also for maximizing the corresponding Vandermonde determinant (Fekete-points) [7].
by using the Vandermonde determinant det([a.sup.i-1.sub.j]) = [[PI].sub.i<j].
Let us introduce the "lacunary" Vandermonde determinant (of type (p + r) x (p +
In order to see the linear independence of the set {[v.sup.n.sub.1], [v.sup.n.sub.2],..., [v.sup.n.sub.p]}, we only need to take n = 0 in Theorem 1.1, then the Casoratian becomes the famous Vandermonde Determinant, i.e.
We denote by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] the Vandermonde determinant [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
In the framework of polynomial interpolation, Fekete points are points that maximize the Vandermonde determinant (in any polynomial basis) on a given compact set and thus ensure that the corresponding Lebesgue constant grows (at most) algebraically, being bounded by the dimension of the polynomial space.
Wybourne, The square of the Vandermonde determinant and its q-generalization, J.
where c [member of] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the vector formed of the [c.sub.j] and F is the vector of function values f(a), a [member of] [A.sub.n] This linear system has a unique solution precisely when the so-called Vandermonde determinant
Both Nair and Chudnovsky used the following weighted version of the Vandermonde determinant
It is easily seen that [V.sub.0]([z.sub.1], ..., [z.sub.k]) is equal to the classical Vandermonde determinant of [z.sub.1], ..., [z.sub.k].