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Title: Optimization of the determinant of the Vandermonde matrix and related matrices

Various techniques for interpolation of data, moment matching in stochastic applications and various methods in numerical analysis can be described using Vandermonde matrices. For this reason the properties of the determinant of the Vandermonde matrix and related matrices are interesting. Here the extreme points of the Vandermonde determinant, and related determinants, on some simple surfaces such as the unit sphere are analyzed, both numerically and analytically. Some results are also visualized in various dimensions. The extreme points of the Vandermonde determinant are also related to the roots of certain orthogonal polynomials such as the Hermite polynomials.
Authors:
; ;  [1]
  1. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Box 883, SE-721 23 Västerås (Sweden)
Publication Date:
OSTI Identifier:
22390796
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1637; Journal Issue: 1; Conference: ICNPAA 2014: 10. International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, Narvik (Norway), 15-18 Jul 2014; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HERMITE POLYNOMIALS; INTERPOLATION; MATRICES; NUMERICAL ANALYSIS; OPTIMIZATION; SPHERES; STOCHASTIC PROCESSES; SURFACES