The field of matrix approximation and linear system solving is witnessing significant developments, with a focus on improving the scalability and efficiency of various techniques in machine learning, uncertainty quantification, and control. Researchers are exploring alternative approaches to traditional SVD-based methods, such as CUR decomposition, which can preserve native matrix structures and facilitate data interpretation. Additionally, there is a growing interest in developing fast and stable algorithms for solving linear systems, including those with concatenated orthogonal matrices and high-condition numbers. Noteworthy papers in this area include: Fast Rank Adaptive CUR via a Recycled Small Sketch, which introduces an adaptive and efficient algorithm for CUR decomposition. Universal Solution to Kronecker Product Decomposition, which provides a general solution for the Kronecker product decomposition of vectors, matrices, and hypermatrices. Relative-Absolute Fusion: Rethinking Feature Extraction in Image-Based Iterative Method Selection for Solving Sparse Linear Systems, which proposes an efficient feature extraction technique to enhance image-based selection approaches. Instability of the Sherman-Morrison formula and stabilization by iterative refinement, which analyzes the backward stability of the Sherman-Morrison formula and proposes a stabilization technique using iterative refinement.