2015 - Spring semester

May 28, 12:00, Room #60
Season-closing internal meeting of sc:ala members

May 21, 12:00, Room #60
Ernest Šanca (Novi Sad): A wider convergence area for the MSTMAOR iteration methods for LCP

In order to solve large sparse linear complementarity problems on parallel multiprocessor systems, modulus-based synchronous two-stage multisplitting iteration methods based on two-stage multisplittings of the system matrices were constructed and investigated by Bai and Zhang (Numerical Algorithms 62, 59–77 2013).These iteration methods include the multisplitting relaxation methods such as Jacobi, Gauss-Seidel, SOR and AOR of the modulus type as special cases. In the same paper the convergence theory of these methods is developed, under the following assumptions: (i) the system matrix is an H+-matrix and (ii) one acceleration parameter is greater than the other. Here we show that the second assumption can be avoided, thus enabling us to obtain an improved convergence area. The result is obtained using the similar technique proposed by Cvetković and Kostić (Numerical Linear Algebra with Applications 21, 534–539 2014), and its usage is demonstrated by an example of the LCP. 

May 7, 12:00, Room #60
Nikola Gradojević (Lille): Heterogeneous investment horizons and realized jump risk in financial markets

April 23, 12:00, Room #60
Miroslav Nikolić, Srđan Milićević (Novi Sad): Inclusion areas for polynomial zeros in generalized bases

Inclusion regions for polynomial zeros expressed in generalized bases are relatively rare, in comparison to those expressed in power bases. Most frequently used techniques for finding aforementioned inclusion regions often rely only on Gershgorin circles, related to the comrade matrices of polynomials. However, some other localization regions can be of use in certain situations. We will present some cases where inclusion regions can be easily obtained, with special emphasis on polynomials in Newton and Chebyshev bases.

April 16, 12:00, Room #60
Vladimir Kostić (Novi Sad): Robust indicators of the stable energetic food webs

After a short review of the contemporary stability indicators recently used to assess behavior of energetic food webs, we present the discovered drawbacks in terms of timescales of transient instability. Then, a novel robust measure that incorporates uncertainty level of empirical data in the stability analysis is introduced. As a result, more realistic notion of stability is achieved, and its usefulness is advocated. Finally, an efficient numerical algorithm for its computation is constructed to allow possible applications to high resolution food webs in the future. New stability indicator is computed for a soil food web and it is compared with the ones reported in the literature. 

April 2, 12:00, Room #60
Igor Dolinka (Novi Sad): Variants of semigroups - the case study of finite full transformation monoids

Abstract (pdf)

March 26, 12:00, Room #60
Vladimir Kostić (Novi Sad): Dynamics and spectral properties. Part IV

March 19, 12:00, Room #60
Vladimir Kostić (Novi Sad): Dynamics and spectral properties. Part III

March 12, 12:00, Room #60
Vladimir Kostić (Novi Sad): Dynamics and spectral properties. Part II

February 26, 12:00, Room #60
Vladimir Kostić (Novi Sad): Dynamics and spectral properties. Part I

This series of lectures is dedicated to understanding of the behaviour of linear time invariant dynamical systems (LTIDS) using spectral theory of matrices. More precisely, first, we will provide an overview of the important results from the last twenty years of research to show how spectra, numerical range and pseudospectra determine the dynamics of LTIDS. Second, linear stability analysis of the general (nonlinear) time invariant dynamical systems occurring in practice will be presented. And, finally, in concluding lectures, the usefulness of these tools in some practical examples from science and industry will be presented.