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Optimization of the Determinant of the Vandermonde Matrix and Related Matrices

Author

Listed:
  • Karl Lundengård

    (Mälardalen University)

  • Jonas Österberg

    (Mälardalen University)

  • Sergei Silvestrov

    (Mälardalen University)

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.

Suggested Citation

  • Karl Lundengård & Jonas Österberg & Sergei Silvestrov, 2018. "Optimization of the Determinant of the Vandermonde Matrix and Related Matrices," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1417-1428, December.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:4:d:10.1007_s11009-017-9595-y
    DOI: 10.1007/s11009-017-9595-y
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