The recent developments in the field of numerical methods and computational mathematics have shown a significant focus on enhancing the efficiency and accuracy of algorithms for solving complex mathematical problems. Innovations include the adaptation of existing methods to new contexts, such as the scaling-and-squaring technique for computing the inverses of matrix $varphi$-functions, and the introduction of adaptive optimization techniques into iterative approximation methods, exemplified by the AdagradLSPIA approach. There is also a notable advancement in the construction and analysis of polynomial meshes on algebraic sets, which has implications for interpolation and approximation tasks. Furthermore, the exploration of optimal properties of tensor products of B-bases and the development of accurate bidiagonal decomposition methods for generalized Pascal matrices highlight the ongoing efforts to improve the conditioning and computational accuracy of numerical algorithms. The field is also witnessing the application of multilevel active subspaces for function approximation, which aims to reduce computational costs while maintaining accuracy. Additionally, the extension of q-Bernstein basis functions to triangular domains and the development of corecursive coding techniques for high computational derivatives and power series represent innovative approaches to handling complex mathematical structures and computations.nn### Noteworthy Papersn- Scaling-and-squaring method for computing the inverses of matrix $varphi$-functions: Introduces an efficient numerical method for computing the inverse of matrix $varphi$-functions, leveraging the Newton-Schulz iteration for matrix inversion.n- AdagradLSPIA: Presents an accelerated version of the LSPIA method, enhanced with adaptive optimization techniques, demonstrating superior performance in tensor product B-spline surface fitting.n- Polynomial meshes on algebraic sets: Offers a general construction of polynomial weakly admissible meshes on compact subsets of algebraic hypersurfaces, with applications in interpolation and least-squares approximation.n- A function approximation algorithm using multilevel active subspaces: Proposes a multilevel version of the Active Subspace method, reducing computational costs for function approximation tasks.n- An evaluation algorithm for q-B'ezier triangular patches formed by convex combinations: Extends q-Bernstein basis functions to triangular domains and introduces a de Casteljau type evaluation algorithm.