The recent advancements in numerical methods and high-dimensional computations have significantly pushed the boundaries of computational efficiency and accuracy. A notable trend is the development of algorithms that leverage low-rank approximations and randomized techniques to handle the complexities of high-dimensional data. These methods are particularly effective in fields such as quantum many-body physics, uncertainty quantification, and image processing. The integration of parallel processing and robust error bounds in these algorithms ensures both computational feasibility and reliability. Additionally, there is a growing focus on the numerical approximation of non-self-adjoint operators and the efficient application of sequences of planar rotations, which are critical for solving nonlinear eigenvalue problems and enhancing the performance of numerical linear algebra algorithms. The unification of Trefftz-like methods provides a comprehensive framework for error analysis and method construction, bridging gaps between local and global problem-solving approaches. Notably, the extension of parallel low-rank matrix integrators to tensor networks and the introduction of efficient randomized algorithms for tensor decomposition mark significant strides in computational mathematics and its applications.