The field of numerical methods is witnessing significant advancements in tackling complex problems. Researchers are developing innovative techniques to improve the efficiency and accuracy of simulations, particularly in areas such as eigenvalue problems, parametric models, and contact mechanics. A notable trend is the integration of experimental data and computational methods to enhance the fidelity of simulations. Additionally, there is a growing focus on developing certified model order reduction methods for large-scale parametric problems. Noteworthy papers include:

• A Hidden Variable Resultant Method for the Polynomial Multiparameter Eigenvalue Problem, which presents a novel global algorithm for solving polynomial multiparameter eigenvalue problems.
• Adaptive hyper-reduction of non-sparse operators, which proposes an adaptive structure-preserving hyper-reduction method for parametric particle-based kinetic plasma models.
• Certified Model Order Reduction for parametric Hermitian eigenproblems, which introduces a novel error estimate for the approximation error related to the eigenspace associated with the smallest eigenvalue. These advancements have the potential to significantly impact various fields, including physics, engineering, and materials science.