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.


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    Title :

    Optimization of the determinant of the Vandermonde matrix and related matrices



    Conference:

    10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 ; 2014 ; Narvik, Norway


    Published in:

    AIP Conference Proceedings ; 1637 , 1 ; 627-636


    Publication date :

    2014-12-10


    Size :

    10 pages





    Type of media :

    Conference paper


    Type of material :

    Electronic Resource


    Language :

    English






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