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Extreme points of the Vandermonde determinant on the sphere and some limits involving the generalized Vandermonde determinantPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2013 (English)Report (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Mälardalen University , 2013. , p. 28
##### Keywords [en]

Vandermonde matrix, Determinants, Extreme points, Unit sphere, Generalized Vandermonde matrix
##### National Category

Mathematical Analysis
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

URN: urn:nbn:se:mdh:diva-23914OAI: oai:DiVA.org:mdh-23914DiVA, id: diva2:682307
#####

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##### Funder

Swedish Research CouncilAvailable from: 2013-12-27 Created: 2013-12-21 Last updated: 2019-06-24Bibliographically approved
##### In thesis

The values of the determinant of Vandermonde matrices with real elements are analyzed both visually and analytically over the unit sphere in various dimensions. For three dimensions some generalized Vandermonde matrices are analyzed visually. The extreme points of the ordinary Vandermonde determinant on finite-dimensional unit spheres are given as the roots of rescaled Hermite polynomials and a recursion relation is provided for the polynomial coefficients. Analytical expressions for these roots are also given for dimension three to seven. A transformation of the optimization problem is provided and some relations between the ordinary and generalized Vandermonde matrices involving limits are discussed.

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3. Extreme points of the Vandermonde determinant and phenomenological modelling with power exponential functions$(function(){PrimeFaces.cw("OverlayPanel","overlay1329454",{id:"formSmash:j_idt786:2:j_idt790",widgetVar:"overlay1329454",target:"formSmash:j_idt786:2:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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