Plenary Lecture

Pseudospectral Structure of the Singular Vectors of Nonstationary Time Series

Profesor Alexander Milnikov
Department of Informatics and Control Systems
Georgian Technical University
Department of Computer Technologies and Engineering
International Black Sea University

Abstract: It is proved, that m principal singular vectors of a matrix , constructed on the base of a time series, contained m periodical deterministic components with additive white noise, have equal pseudospectrums and their pseuvdospectral structure is identical to the time series’ one. Exact definitions of a conception of the pseuvdospectral structures are introduced, as well as a numerical criterion of their identity. Detecting of singular vectors having identical pseuvdospectral structures allows predefining the number of periodical deterministic components and separating principal and the other singular components from each other.

Brief Biography of the Speaker: A. Milnikov holds a Bs/Ms in Electronic Engineering, a PhD in Electric Engineering (1978) and a Doctor of Sciences in Applied Mathematics (2002) from the Technical University of Georgia.
He works as a full professor of: International Black Sea University (Tbilisi, Georgia) (1994-present), Technical University of Georgia (1999-present), Georgian Academy of Scineces, Institute of Applied Mechanics (1980-present), Academician (1980-1988), Leading Academician (1989-2005), Principal Academician (2005-present). Also he worked as a Dean of the Computer Technologies and Engineering Faculty at the International Black Sea University (1994-2008). His research interests include: the Electrical Circuits Theory, Modern Geometry (Differential Geometry and Tensorial Analysis), Statistics, Random Processes, Signals Theory and Digital Processing, Filters Design. He has more than 80 publications, qmong them 10 in impact journals, 15 proceedings in WSEAS and Other International Conferences.