The field of numerical methods for linear inverse problems and matrix approximations is witnessing significant developments, driven by the need for efficient and accurate solutions to complex problems. Researchers are exploring new approaches to improve the performance of existing methods, such as the quasi-minimal residual method, and developing innovative techniques like hierarchical Tucker low-rank matrices and adaptive randomized algorithms. These advancements have the potential to impact various applications, including image processing, information retrieval, and scientific simulations. Noteworthy papers in this area include: The paper On the Choice of Subspace for the Quasi-minimal Residual Method for Linear Inverse Problems, which analyzes the impact of subspace selection on solution quality and demonstrates the effectiveness of range restricted QMR. The paper Hierarchical Tucker Low-Rank Matrices: Construction and Matrix-Vector Multiplication, which proposes a new matrix format for approximating non-oscillatory kernel functions and achieves linear complexity. The paper Fast adaptive tubal rank-revealing algorithm for t-product based tensor approximation, which introduces an adaptive randomized algorithm for tubal rank revelation in data tensors and provides theoretical guarantees for its performance.