The field of numerical methods and linear algebra is witnessing significant developments, with a focus on improving the efficiency and accuracy of algorithms for various applications. Researchers are exploring new approaches to linear algebraic tasks, such as kernel density estimation, to reduce computational complexity and improve performance. Additionally, there is a growing interest in developing novel numerical methods for solving nonlinear problems, including nonlinear eigenvalue problems and degenerate cross-diffusion systems. These advancements have the potential to impact a wide range of fields, from computational quantum mechanics to machine learning. Noteworthy papers include:

• A study on using kernel density estimation for linear algebraic tasks, which improves upon existing algorithms and reduces computational complexity.
• A proposal for a novel family of explicit low-regularity exponential integrators for the nonlinear Schrödinger equation, which combines a resonance-based scheme with a dynamically adjusted relaxation parameter.
• A development of a linearization for nonlinear eigenvalue problems with quadratic rational eigenvector nonlinearities, which enables the use of structure exploiting algorithms to improve convergence and reliability.