*(organiser: Mohammad Adm, Palestine Polytechnic University, Hebron & Jürgen Garloff, University of Applied Sciences and University of Konstanz)*

The concept of total positivity is rooted in classical mathematics where it can be traced back to works of Schoenberg on variation diminishing properties and of Gantmacher and Krein on small oscillations of mechanical systems. Since then the class of totally positive matrices and operators proved to be relevant in such a wide range of applications that over the years many distinct approaches to total positivity, amenable to a particular notion, have arisen and advocated by many prominent mathematicians. This area is, however, not just a historically significant subject in mathematics, but the one that continues to produce important advances and spawn worth-wile applications. This is reflected by the topics which will be covered by the speakers of the Special Session, viz. the study of classes of matrices related to total positivity and more generally, to sign regularity, accurate computations based on bidiagonalization, inverse eigenvalue problems, and the location of the roots of polynomials.

*(organiser: Aljosa Peperko, University of Ljubljana, Slovenia & Sergei Sergeev, University of Birmingham, UK)*

Tropical matrix algebra is a vibrant new area in mathematics, which has been developing since 1960's. The motivations of tropical matrix algebra are both applied (in particular, theory of optimal scheduling and discrete event systems) and pure, as there is a correspondence principle (Litvinov and Maslov) saying that every useful result and construction of traditional mathematics over fields might have a useful tropical counterpart. Therefore, tropical mathematics events traditionally bring together mathematicians of various backgrounds, both pure and applied. The emphasis of this workshop will be on new useful constructions in tropical matrix algebra, and possibly also on the influence of tropical geometry.

*(organizer: Takeshi Ogita, Tokyo Woman's Christian University & Siegfried M. Rump, Hamburg University of Technology)*

This special session is devoted to verified numerical computations, in

particular, verification methods for linear algebra, optimization, and

even for ordinary differential equations. Since verified numerical

computations enable us to rigorously solve mathematical problems by

numerical methods in pure floating-point arithmetic, they became

increasingly important in a wide range of science and engineering. The

main objective of the special session is to discuss several recent

topics on verification methods and related numerical analysis and matrix

methods.

*(organiser: Milan Hladík, Charles University, Prague)*

Interval computation is a discipline addressed to handling and computing with interval data. The fundamental property of interval computation is the "enclosing property", guaranteeing that all possible realizations of interval data and all roundoff errors are taken into account. Due to this property, interval computation is an important technique for obtaining rigorous results, and for this reason it is used in numerical analysis, global optimization, constraint programming and many other areas. The key object in interval computation is an interval matrix, which is by definition a set of matrices lying entrywise between two given lower and upper bound matrices. This special session will be devoted to investigation of various properties of interval matrices, including theoretical characterization, developing efficient algorithms, classification in the computational complexity sense, and related problems such as solving interval linear systems of equations.