The field of numerical methods for linear systems and optimization is experiencing significant developments, driven by the need for efficient and accurate solutions to complex problems. A key direction is the improvement of preconditioned conjugate gradient methods, which are being enhanced to handle mixed precision and low-rank approximations, leading to faster and more accurate solutions. Another area of focus is the development of GPU-accelerated algorithms, which are being applied to various problems, including Gaussian Process Regression and power system optimization, resulting in significant speedups. Additionally, researchers are exploring new approaches to eigenvalue computation, such as the enhanced shifted QR algorithm, and investigating the use of high-precision arithmetic and quasi multi-word algorithms to improve the accuracy of sparse iterative solvers. Noteworthy papers include: The paper on nuGPR, which proposes a new framework for Gaussian Process Regression that reduces computation cost and achieves significant speedups. The paper on ExaModelsPower.jl, which introduces an open-source modeling library for creating GPU-compatible nonlinear AC optimal power flow models and demonstrates significant speedups compared to alternative tools.