Author, Institution: Rasa Šmidtaitė, Kaunas University of Technology
Science Area, Field of Science: Physical Sciences, Informatics – 09P
Scientific Supervisor: Prof. Dr. Zenonas NAVICKAS (Kaunas University of Technology, Physical Sciences, Informatics – 09P).
Dissertation Defense Board of Informatics Science Field:
Prof. Dr. Habil. Rimantas BARAUSKAS (Kaunas University of Technology, Physical Sciences, Informatics – 09P) – chairman;
Prof. Dr. Habil. Gintautas DZEMYDA (Vilnius University, Physical Sciences, Informatics – 09P);
Prof. Dr. Eugenijus KANIUŠAS (Vienna University of Technology, Physical Sciences, Informatics – 09P);
Assoc. Prof. Dr. Kristina LUKOŠEVIČIŪTĖ (Kaunas University of Technology, Physical Sciences, Informatics – 09P);
Prof. Dr. Alfonsas MISEVIČIUS (Kaunas University of Technology, Physical Sciences, Informatics – 09P).
The Doctoral Dissertation is available and at the libraries of Kaunas University of Technology (K. Donelaičio St. 20, Kaunas) and Vytautas Magnus University (K. Donelaičio g. 52, Kaunas)
Annotation:
The concept of structural matrix decomposition in nonlinear systems analysis is developed in this dissertation. Special three component decomposition of second order matrices was introduced. Special matrix decomposition enabled to simplify formula for matrix n power and to derive the necessary and sufficient conditions for two matrices to commute. The scalar variable in an iterative map was replaced with a second order square matrix. An iterative map of matrices shows new dynamical properties. Modified class of iterative maps of matrices was formed. The necessary and sufficient conditions were derived for the divergence of such iterative maps. The ideas of structural matrix analysis were adapted to the phenomenological human as a complex system model. Novel estimates based on structural matrix analysis were introduced for evaluation of two signal coherence. Later the more general application was introduced – the relation between heart rate variability and Earth local magnetic field was analysed.
Even though relevance is largely determined by practical applications, the basis for this work is a specific structural decomposition of the second order matrix which enabled not only introduce special efects in the iterative maps of matrices but also found application in real-world signals analysis.
