Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Author:
Poulidis Nikolaos
Supervisors info:
Μαριλένα Μητρούλη, Καθηγήτρια, Τμήμα Μαθηματικών, ΕΚΠΑ
Ευαγγελία Κόττα-Αθανασιάδου, Αναπληρώτρια Καθηγήτρια, Τμήμα Μαθηματικών, ΕΚΠΑ
Μιχαήλ Δρακόπουλος, Επίκουρος Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Ελάχιστα Τετράγωνα: Αλγόριθμοι και Εφαρμογές
Translated title:
Least Squares: Algorithms and Applications
Summary:
This thesis is an algorithmic introduction to the least-squares method and its applications. Firstly, the basic concepts are presented along with proofs of useful propositions and the necessary notation that will be needed later is introduced. Following is the definition of the linear least-squares problem(LLSP) and the proof of the existence of a solution. QR factorization of a matrix via Householder transformations is used to solve the LLSP and its implementation algorithm is described in detail. Next, the concepts of the overdetermined LLSP and the underdetermined LLSP are defined while ways of solving them are presented. Finally, the LLSP is applied to polynomial and spline interpolation.
Main subject category:
Science
Keywords:
norm, matrix, linear least-squares problem, Householder transformations, QR factorization
