Optimization of the Determinant of the Vandermonde Matrix and Related Matrices

Karl Lundengård (), Jonas Österberg () and Sergei Silvestrov ()
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Karl Lundengård: Mälardalen University
Jonas Österberg: Mälardalen University
Sergei Silvestrov: Mälardalen University

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 4, 1417-1428

Abstract: 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.

Keywords: Vandermonde determinant; Optimization; Gröbner basis; Orthogonal polynomials; Ellipsoid; Optimal experiment design; Homogeneous polynomials; 33C45; 11C20; 15B99; 08B99 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11009-017-9595-y

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