Methods and algorithms of linear algebra and matrix analysis are important in themselves and also because they are often used in many other areas of pure and applied mathematics, as well as in many other scientific disciplines. As a consequence, linear algebra and its applications is a well established and very active area of research. This statement is clearly supported by the prestigious journals that are specifically focused on this discipline (among them Linear Algebra and its Applications, Numerical Linear Algebra with Applications, and SIAM Journal on Matrix Analysis and Applications), by the number of periodic relevant international conferences devoted to Linear Algebra (such as the series of Householder Symposia, the series of Conferences of the International Linear Algebra Society, and the series of SIAM Conferences on Applied Linear Algebra, just to mention a few of them), and by the numerous research groups developing an exciting, novel, and continuous activity in Linear Algebra all over the world. In this scenario, many groups in Italy and Spain are nowadays working on a wide variety of modern open problems in linear algebra, which range from core problems in matrix analysis to the development of new and efficient numerical algorithms and their applications. The main goal of this special session is to show to researchers in other areas of mathematics how relevant is the activity of the linear algebra community. For this purpose, we propose an special session organized into 4 homogeneous sessions devoted to 4 current hot topics in linear algebra, on which several groups from Italy and Spain are particularly active. These 4 sessions are:

• Applications of preconditioners.
• Matrix equations.
• Polynomial and nonlinear eigenvalue problems.
• Structured matrices.

• Dario Andrea Bini (University of Pisa, Italy)
• Froilán M. Dopico (Charles III University of Madrid, Spain) - dopico@math.uc3m.es
• Silvia Marcaida (University of the Basque Country, Spain)
• Valeria Simoncini (University of Bologna, Italy)

Below you can download the schedule and the abstracts of all talks of this special session.

• Luca Bergamaschi (University of Padova, Italy)

         Tuned preconditioners for iterative SPD eigensolvers

• Rafael Bru (Polytechnic University of Valencia, Spain)

           Preconditioners based on the ISM factorization

• Fernando de Terán (Charles III University of Madrid, Spain)

           Polynomial root-finding using Fiedler companion matrices

• Daniela Di Serafino (Second University of Naples, Italy)

          Updating constraint preconditioners for KKT systems via low-rank correction and scaling techniques

• Bruno Ianazzo (University of Perugia, Italy)

           Algorithms for matrix functions arising from matrix equations

• Nicola Mastronardi (CNR, Bari, Italy)

           On solving KKT linear systems arising in Model Predictive Control viarecursive anti- triangular factorization

• Karl Meerbergen (KU Leuven, Belgium)

          CORK: A compact Rational Krylov method for solving the nonlinear eigenvalue problem

• Beatrice Meini (University of Pisa, Italy)

          Computing the exponential of a large block triangular block Toeplitz matrix

• Julio Moro (Charles III University of Madrid, Spain)

          First order expansions for eigenvalues of multiplicatively perturbed matrices

• Vanni Noferini (University of Manchester, United Kingdom)

           Tropical roots as approximations of eigenvalues of regular matrix polynomials

• Juan Manuel Peña (University of Zaragoza, Spain)

          Accurate computations for subclasses and superclasses of totally positive matrices

• Federico Poloni (University of Pisa, Italy)

          Multivariate time series estimation via projections and matrix equations

• Margherita Porcelli (University of Bologna, Italy)

           Robust Preconditioners for Optimal Control problems with State and Control Constraints

• Francoise Tisseur (University of Manchester, United Kingdom)

           Recent advances in the numerical solution of dense polynomial eigenvalue problems

• Raf Vandebril (KU Leuven, Belgium)

          Roots of polynomials: a new fast QR algorithm

• Ion Zaballa (University of the Basque Country, Spain)

          Coprime Rational Matrix Functions and Equivalence