2015 - Autumn semester

December 10, 12:00, Room #60
Igor Dolinka (Novi Sad): Linear sandwich semigroups
[ slides (pdf) ]

Let M_mn denote the set of all m x n matrices over a field F, and fix some n x m matrix A from M_nm. An associative operation * may be defined on M_mn by X*Y=XAY for all X,Y from M_mn, and the resulting "sandwich semigroup" is denoted by M^A_mn. It seems these linear sandwich semigroups were introduced by Lyapin in his 1960 monograph, and they are related to the so-called generalized matrix algebras of Brown (1955), but they have not received a great deal of attention since some early papers by Magill and Subbiah in the 60s and 70s. In this talk, I will report on joint work with James East (Sydney) in which we investigate certain combinatorial questions regarding the linear sandwich semigroups, including: regularity, Green's relations, ideals, rank and idempotent rank. We also outline a general framework for studying more general sandwich semigroups: the context is a kind of partial semigroup related to Ehresmann-style arrows-only categories.

November 26, 12:00, Room #60
Zagorka Lozanov-Crvenković (Novi Sad): A report from Rio: The 60th World Statistics Congress

November 19, 12:00, Room #60
Ernest Šanca (Novi Sad): A wider convergence area for the MSTMAOR iteration methods for LCP - MatTriad 2015 report
[ slides (pdf) ]

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. 

November 12, 12:00, Room #60
Maja Nedović (Novi Sad): H-matrix theory and applications - MatTriad 2015 report
[ slides (pdf) ]

The theory of M- and H-matrices plays an important role in applied linear algebra. It is one of the basic tools for researchers dealing with eigenvalue localization problems, analysis of iterative methods for solving large systems of linear equations, and related topics. In this talk, different matrix properties that guarantee nonsingularity of matrices and define different subclasses of H-matrices will be presented together with related results concerning Schur complement matrices, eigenvalue localization and bounds for the max-norm of the inverse matrix. 

November 5, 12:00, Room #60
Season-opening internal meeting of sc:ala members