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- Title
Optimization of the Determinant of the Vandermonde Matrix and Related Matrices.
- Authors
Lundengård, Karl; Österberg, Jonas; Silvestrov, Sergei
- Abstract
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 Gröbner 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.
- Subjects
VANDERMONDE matrices; MATHEMATICAL optimization; LAGRANGE multiplier; GROBNER bases; POLYNOMIALS
- Publication
Methodology & Computing in Applied Probability, 2018, Vol 20, Issue 4, p1417
- ISSN
1387-5841
- Publication type
Article
- DOI
10.1007/s11009-017-9595-y