Unit:
Κατεύθυνση Διοίκηση, Αναλυτική και Πληροφοριακά Συστήματα ΕπιχειρήσεωνLibrary of the Faculty of Economics and of the Faculty of Business Administration
Supervisors info:
Ιωάννης Δημητρίου, Καθηγητής, Τμήμα Οικονομικών Επιστημών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Original Title:
Numerical Evidence of the Lagrange Multipliers in Piecewise Monotonic Data Approximation Method
Translated title:
Numerical Evidence of the Lagrange Multipliers in Piecewise Monotonic Data Approximation Method
Summary:
This thesis investigates the behavior of the Lagrange multipliers at the piecewise monotonic approximation to spectra of minerals, carbohydrate and thyroid hormone. The spectra datasets of minerals are provided freely from Labratory of Photoinduced Effects Vibrational and X-RAY Spectroscopies [25], of thyroid hormone from Human Metabolome Database [26] and of carbohydrate from SPECARB database [27]. The thesis consists of four chapter. In chapter 1 we present the problem of data approximation and especially the case of least squares data fitting, how the smoothed data are calculated and expound the piecewise monotonic data approximation. Furthermore, we discuss the non-linear programming problem and Lagrange multipliers in both cases when the constraints are linear equality and linear inequality. In chapter 2 we present the piecewise monotonic data approximation method, we give an example and we state how the Lagrange multipliers are calculated. In chapter 3 we perform experiments using nine Raman spectra, eight of minerals and one of carbohydrate, and one MS spectrum of thyroid hormone in order to determine how Lagrange multipliers are changed as the number of monotonic sections in a piecewise monotonic data approximation is changed. We define the measures which are needed to determine this relationship, we fit each data by the L2WPMA software package for various values of monotonic sections and we present the results. In chapter 4 we present the conclusions from the experiments which lead to develop a Lagrange multiplier test that will provide an estimation of a suitable or adequate number of monotonic sections of the fit.
Main subject category:
Science
Keywords:
Data smoothing, Least squares method, Lagrange multipliers, Piecewise monotonic data approximation, L2WPMA algorithm
