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Optimization of the determinant of the Vandermonde matrix on the sphere and related surfaces
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (Mathematics and Applied Mathematics)ORCID iD: 0000-0003-3204-617X
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (Mathematics and Applied Mathematics)
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (Mathematics and Applied Mathematics)ORCID iD: 0000-0003-4554-6528
2015 (English)In: ASMDA 2015 Proceedings: 16th Applied Stochastic Models and Data Analysis International Conference with 4th Demographics 2015 Workshop / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2015, 637-648 p.Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology , 2015. 637-648 p.
Keyword [en]
Vandermonde determinant, optimization, Gr¨obner basis, orthogonal polynomials, ellipsoid, optimal experiment design, homogeneous polynomials
National Category
Mathematical Analysis
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-29938DOI: www.asmda.es/images/1_L-MOH_ASMDA2015_Proceedings.pdfISBN: 978-618-5180-05-8 (print)OAI: oai:DiVA.org:mdh-29938DiVA: diva2:882741
Conference
16th Applied Stochastic Models and Data Analysis International Conference (ASMDA2015) with Demographics 2015 Workshop, 30 June – 4 July 2015, University of Piraeus, Greece
Available from: 2015-12-15 Created: 2015-12-15 Last updated: 2017-02-14Bibliographically approved
In thesis
1. Generalized Vandermonde matrices and determinants in electromagnetic compatibility
Open this publication in new window or tab >>Generalized Vandermonde matrices and determinants in electromagnetic compatibility
2017 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpful for solving many kinds of problems. In this thesis we will discuss this matrix and some of its properties as well as a generalization of it and how it can be applied to curve fitting discharge current for the purpose of ensuring electromagnetic compatibility.

In the first chapter the basic theory for later chapters is introduced. This includes the Vandermonde matrix and some of its properties, history, applications and generalizations, interpolation and regression problems, optimal experiment design and modelling of electrostatic discharge currents with the purpose to ensure electromagnetic compatibility.

The second chapter focuses on finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids, cylinders and tori. The extreme points are analysed in three dimensions or more.

The third chapter discusses fitting a particular model called the p-peaked Analytically Extended Function (AEF) to data taken either from a standard for electromagnetic compatibility or experimental measurements. More specifically the AEF will be fitted to discharge currents from the IEC 62305-1 and IEC 61000-4-2 standards for lightning protection and electrostatic discharge immunity as well as some experimentally measured data of similar phenomena.

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2017
Series
Mälardalen University Press Licentiate Theses, ISSN 1651-9256 ; 253
National Category
Mathematics Mathematical Analysis Computational Mathematics Probability Theory and Statistics Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-34864 (URN)978-91-7485-312-4 (ISBN)
Presentation
2017-03-23, Kappa, Västerås, 13:15 (English)
Opponent
Supervisors
Available from: 2017-02-14 Created: 2017-02-14 Last updated: 2017-03-14Bibliographically approved

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CiteExportLink to record
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Citation style
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