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Optimization of the determinant of the Vandermonde matrix on the sphere and related surfaces
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)ORCID-id: 0000-0003-3204-617X
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)ORCID-id: 0000-0003-0586-1320
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)ORCID-id: 0000-0003-4554-6528
2015 (Engelska)Ingår i: 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, s. 637-648Konferensbidrag, Publicerat paper (Refereegranskat)
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.

Ort, förlag, år, upplaga, sidor
ISAST: International Society for the Advancement of Science and Technology , 2015. s. 637-648
Nyckelord [en]
Vandermonde determinant, optimization, Gr¨obner basis, orthogonal polynomials, ellipsoid, optimal experiment design, homogeneous polynomials
Nationell ämneskategori
Matematisk analys
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
URN: urn:nbn:se:mdh:diva-29938ISBN: 978-618-5180-05-8 (tryckt)OAI: oai:DiVA.org:mdh-29938DiVA, id: diva2:882741
Konferens
16th Applied Stochastic Models and Data Analysis International Conference (ASMDA2015) with Demographics 2015 Workshop, 30 June – 4 July 2015, University of Piraeus, Greece
Tillgänglig från: 2015-12-15 Skapad: 2015-12-15 Senast uppdaterad: 2018-03-05Bibliografiskt granskad
Ingår i avhandling
1. Generalized Vandermonde matrices and determinants in electromagnetic compatibility
Öppna denna publikation i ny flik eller fönster >>Generalized Vandermonde matrices and determinants in electromagnetic compatibility
2017 (Engelska)Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Västerås: Mälardalen University, 2017
Serie
Mälardalen University Press Licentiate Theses, ISSN 1651-9256 ; 253
Nationell ämneskategori
Matematik Matematisk analys Beräkningsmatematik Sannolikhetsteori och statistik Algebra och logik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-34864 (URN)978-91-7485-312-4 (ISBN)
Presentation
2017-03-23, Kappa, Västerås, 13:15 (Engelska)
Opponent
Handledare
Tillgänglig från: 2017-02-14 Skapad: 2017-02-14 Senast uppdaterad: 2017-09-28Bibliografiskt granskad

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http://www.asmda.es/images/1_L-MOH_ASMDA2015_Proceedings.pdf

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Lundengård, KarlSilvestrov, Sergei

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Lundengård, KarlÖsterberg, JonasSilvestrov, Sergei
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