2014 - Spring semester

May 29, 12:00, Room #60
Semester-closing meeting of sc:ala members.

May 8, 12:00, Amphitheatre I
Zhong-Zhi Bai (Beijing): Modulus-based parallel multisplitting iteration methods for linear complementarity problems

In order to solve large sparse linear complementarity problems on parallel multiprocessor systems, by making use of the modulus reformulation of the target problems and the multiple splittings of the system matrices we design the parallel modulus-based matrix splitting iteration methods, the modulus-based matrix splitting two-stage iteration methods and their relaxed variants. We prove the asymptotic convergence of these matrix multisplitting iteration methods for the H-matrices of positive diagonal entries, and give numerical results to show the feasibility and effectiveness of the modulus-based matrix multisplitting iteration methods when they are implemented in the parallel computational environments. 

13:00 PM, Amphitheatre I
Lev A. Krukier (Rostov-on-Don): Symmetric & skew-symmetric splitting and iterative methods

April 3, 12:00, Room #60
Vladimir Kostić (Novi Sad): On matrix operators on sequence spaces and their spectra

We will investigate spectra of infinite matrices that can act as a linear operators from the Banach space l^p to itself. To that end, we will propose method that is based on a generalization of a strict diagonal dominance of infinite matrices that is adapted to l^p and l^q norms, for a Holder pair p and q. Results are illustrated with several examples, and some interesting applications are discussed. 

March 27, 12:00, Room #60
Ksenija Doroslovački (Novi Sad): Generalized diagonal dominance for block matrices and possibilities of its application

This talk relates to matrices written in their block form. New knowledge about properties of such matrices, based on the idea of generalized diagonal dominance, is the main goal of this talk. Motivation lies primarily in possible applications to very actual investigations, not only within other areas of applied and numerical linear algebra, but also in engineering, medicine, pharmacy, ecology, economics and other sciences.

In this talk, we will explain two possible ways of block generalizations and highlight their relationship. We will also present an application to estimation of max norm of the inverse matrix. At first, an overview of the results in the point-wise case is given, then, the block case is discussed. Numerical examples are chosen to illustrate relations between various estimations, but more important, to show the efficiency of every new estimation.

March 20, 12:00, Room #60
Maja Nedović (Novi Sad): Scaling technique for (Σ-)Nekrasov matrices

The aim of this talk is to present one way of constructing a scaling matrix for a (Σ-)Nekrasov matrix and, using the scaling approach, to obtain a Geršgorin-type eigenvalue localization for the corresponding Schur complement matrix.

March 6 & 13, 12:00, Room #60
Vladimir Kostić (Novi Sad): On matrix nearness problems: distance to delocalization/localization (Part I-II)

Numerous problems in mechanics, mathematical physics, and engineering can be formulated as eigenvalue problems where the focus is, after determining that the eigenvalues are in the specific desirable domain, to detect minimal size of perturbation that will cause the eigenvalues to leave the domain. The most frequent of such domains are connected to stability of dynamical systems: open left half-plane of the complex plane (continuous dynamical systems) and open unit disk (discrete dynamical systems). While the matrix nearness problems connected to stability have lately been extensively investigated, robustness of spectral inclusions by other domains (that arise for example in acoustic field computations) has remained out of focus.

In this talk, we will consider eigenvalue localization sets of Lyapunov-type which generalize notion of instability/stability to more complicated domains (half-planes, circles, ellipses, rings, Cassini ovals, lemniscates, strips, cardioids, etc.). Then, we formulate two matrix nearness problems: distance to delocalization and distance to localization, and discuss methods for their solution.

Finally, we present numerical method that computes distance to delocalization for Lyapunov-type localization domains. The algorithm that we provide is based on pseudospectral properties, implicit determinant approach and uses Newton’s method in order to optimize minimal singular value over an algebraic curve defined by a Hermitian function in the complex plane.

February 27, 12:00, Room #60
Ljiljana Cvetković (Novi Sad): Geršgorin-type diamonds