Optimization of the Determinant of the Vandermonde Matrix and Related Matrices

• The value of the Vandermonde determinant is optimized over various surfaces, including the sphere, ellipsoid and torus. Lagrange multipliers are used to find a system of polynomial equations which give the local extreme points in its solutions. Using Grobner basis and other techniques the extreme points are given either explicitly or as roots of polynomials in one variable. The behavior of the Vandermonde determinant is also presented visually in some interesting cases.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

Keyword

Vandermonde determinant

Optimization

Grobner basis

Orthogonal polynomials

Ellipsoid

Optimal experiment design

Homogeneous polynomials

33C45

11C20

15B99

08B99

Mathematics/Applied Mathematics

matematik/tillämpad matematik

Publication and Content Type

ref (subject category)

art (subject category)