This Symposium was the nineteenth in a series, previously called the Gatlinburg Symposia, and was hosted by the Université catholique de Louvain and the Katholieke Universiteit Leuven. The location of the event was the Sol-Cress conference site in Spa, Belgium. The local organizers were Paul Van Dooren (chair) and Pierre-Antoine Absil from UCL, Sabine Van Huffel, Karl Meerbergen and Marc Van Barel from KULeuven and Annick Sartenaer from the Université de Namur. The steering committee, responsible for the scientific part of the meeting, were Jim Demmel (UC Berkeley, USA), Alan Edelman (MIT, USA), Heike Fassbender (TU Braunschweig, Germany), Ilse Ipsen (chair) (NC State, USA), Volker Mehrmann (TU Berlin, Germany), Jim Nagy (Emory Univ USA), Yousef Saad (Univ Minnesota USA), Valeria Simoncini (Univ Bologna, Italy), Zdenek Strakos (Charles Univ Prague, Czech Republic) and Andy Wathen (Oxford Univ UK).

Attendance at the meeting is traditionally by invitation only. Applications were solicited from researchers in numerical linear algebra, matrix theory, and related areas such as optimization, differential equations, signal processing, and control. This meeting had a record of 289 applications of which 157 participants were selected, but about a dozen of them could not attend. Part of the success of the meeting is due to the fact that the organizers made sure to have a nice blend of younger and more experienced speakers in the plenaries as well as in the parallel sessions and the poster presentations. The usual random seating at the evening dinners helped to break the ice between young attendees and more senior researchers and made sure that there were a lot of interactions between them. Talks and poster sessions were very well attended, despite the quite busy schedule.

The Symposium aims to be very informal and tries to encourage intermingling of young and established researchers. All participants attended the entire meeting and were given a time slot for presentation of their research results. These were either plenary presentations, somewhat shorter presentations in parallel sessions or short "blitz" presentations inviting everybody to come and listen to their poster explanation. These poster presentations with "blitz intro" were very successful and the best posters were given a special award at the end of the meeting. The prize winners were Andreas Frommer (Convergence of restarted Krylov subspace methods for matrix functions) and Tyrone Rees (Preconditioning linear systems arising in constrained optimization problems). Honorable mentions were given to David Titley-Peloquin (On the sensitivity of matrix functions to random noise) and Sabine Le Borne (Hierarchical preconditioners for higher order FEM). The prize committee consisted of Alison Ramage, Chen Greif, Daniel Kressner and Zlatko Drmac.

A high point of the meeting was the awarding of the 15th triennial Alston Householder Award, for the best PhD dissertation in numerical linear algebra submitted in 2011-2014. This year there were two co-winners: Nicolas Gillis (Univ. Cath. Louvain, Belgium) with a thesis entitled "Nonnegative matrix factorization : complexity, algorithms and applications" and Yuji Nakatsukasa (University of Tokyo, Japan) with the thesis entitled "Algorithms and Perturbation Theory for Matrix Eigenvalue Problems and the Singular Value Decomposition". The award committee also gave honorable mentions to the following two theses: Cédric Effenberger (EPFL, Switzerland) for the thesis "Robust solution methods for nonlinear eigenvalue problems" and Saifon Chaturantabut (Rice University, USA) for the thesis "Nonlinear Model Reduction via Discrete Empirical Interpolation". The Householder Award committee consisted of Michele Benzi, Inderjit Dhillon, Howard Elman, Volker Mehrmann (chair), Françoise Tisseur and Steven Vavasis.

The Householder Symposium was sponsored by several organizations and companies: Mathworks, NAG, FNRS, ILAS, DYSCO and SIAM all contributed to the success of this meeting via their financial support. This allowed us to cover most of the organizational expenses and to provide partial support to some early career attendees and to participants from countries with limited resources. Their support was very much appreciated and contributed to the success of the meeting.


Paul Van Dooren