Mälardalen University Doctoral Dissertation 327 Asaph Keikara Muhumuza Extreme points of the Vandermonde determinant in numerical EXTREME POINTS OF THE VANDERMONDE DETERMINANT IN NUMERICAL APPROXIMATION, RANDOM MATRIX THEORY AND FINANCIAL MATHEMATICS approximation, random matrix theory and financial mathematics Asaph Keikara Muhumuza Address: P.O. Box 883, SE-721 23 Västerås. Sweden ISBN 978-91-7485-484-8 2020 Address: P.O. Box 325, SE-631 05 Eskilstuna. Sweden E-mail:
[email protected] Web: www.mdh.se ISSN 1651-4238 1 Mälardalen University Press Dissertations No. 327 EXTREME POINTS OF THE VANDERMONDE DETERMINANT IN NUMERICAL APPROXIMATION, RANDOM MATRIX THEORY AND FINANCIAL MATHEMATICS Asaph Keikara Muhumuza 2020 School of Education, Culture and Communication 2 Copyright © Asaph Keikara Muhumuza, 2020 ISBN 978-91-7485-484-8 ISSN 1651-4238 Printed by E-Print AB, Stockholm, Sweden 3 Mälardalen University Press Dissertations No. 327 EXTREME POINTS OF THE VANDERMONDE DETERMINANT IN NUMERICAL APPROXIMATION, RANDOM MATRIX THEORY AND FINANCIAL MATHEMATICS Asaph Keikara Muhumuza Akademisk avhandling som för avläggande av filosofie doktorsexamen i matematik/tillämpad matematik vid Akademin för utbildning, kultur och kommunikation kommer att offentligen försvaras måndagen den 14 december 2020, 15.15 i Lambda +(digitalt Zoom), Mälardalens Högskola, Västerås. Fakultetsopponent: Docent Olga Liivapuu, Estonian University of Life Sciences Akademin för utbildning, kultur och kommunikation 4 Abstract This thesis discusses the extreme points of the Vandermonde determinant on various surfaces, their applications in numerical approximation, random matrix theory and financial mathematics. Some mathematical models that employ these extreme points such as curve fitting, data smoothing, experimental design, electrostatics, risk control in finance and method for finding the extreme points on certain surfaces are demonstrated.