TNC'18:Editor's Preface

This volume contains the articles presented at TNC 2018, the first International Workshop on  Trusted Numerical Computations, which was held on June 19, 2018, in Krakow, Poland. TNC 2018 took place as a collocated event of the second International Conference on Emerging Trends in Applied Mathematics and Mechanics, ETAMM 2018.

The aim of the TNC workshop is to provide a forum for researchers who are interested in the quality of numerical computations or the results of simulations which may be impacted with method and round-off errors. In particular, numerical quality impacts the execution time, reproducibility and general performances, especially when dealing with sensitive functions such as the ones that we can find in applied mathematics and mechanics, when considering problems in physics, engineering sciences, biology, economy, etc. The design, verification and optimization of numerical software becomes a strong challenge to guarantee the soundness and the efficiency of computations. To cope with numerical issues, to know how to measure and minimize errors or to imagine other ways to better refine meshes, the formal verification of numerical simulations is mandatory. The TNC minisymposium intends to be a step toward this design, verification and optimization and, more generally, toward the definition of trusted numerical computations.

The topics of interest include, but are not limited to:

Computer-aided verification of numerical computations
Correct-by-construction numerical methods
Approximations in numerical simulations
Optimization of numerical algorithms
Numerical accuracy in simulations for biology, physics, economy, etc.
Specifications of correctness for numerical programs
Verification and optimization of numerical programs
Computations of numerical properties (interval methods, automatic differentiation, etc.)
Formal methods for numerical codes (abstract interpretation, formal proofs, model checking, etc.)
This year we accepted  6 submissions for presentation during the minisymposium and inclusion in these proceedings. Each of these submissions went through a rigorous review process in which each paper received at least two reports. The minisymposium also featured invited talks by Warwick Tucker (Professor, Uppsala University, Sweden) and Milan Hladik (Associate Professor, Charles University, Czech Republic).

We would like to thank the TNC minisymposium chairs. We would like also to thank the ETAMM 2018 workshop chair Stanislaw Migorski for his help with the local arrangements in Krakow. We would like to thank the Program Committee members and reviewers for their useful and detailed reviews and discussions, all authors for their submissions, and all attendees of the workshop.

Matthieu Martel
Nasrine Damouche
Julien Alexandre-Dit-Sandretto
June 2018