The field of numerical methods and computational techniques is witnessing significant advancements, driven by the need for more efficient and accurate solutions to complex problems. Researchers are focusing on developing innovative methods that can tackle challenging issues such as nonlinear systems of equations, low-SNR data, and ill-conditioned linear systems. A key direction in this field is the integration of machine learning and neural networks to accelerate iterative methods and improve convergence rates. Additionally, there is a growing emphasis on developing stable and robust algorithms that can handle high-performance computing solutions for large-scale linear systems. Noteworthy papers in this area include:

• A stochastic column-block gradient descent method that outperforms existing methods for solving nonlinear systems of equations.
• A 3-Dimensional CryoEM Pose Estimation and Shift Correction Pipeline that leverages multi-dimensional scaling techniques and robust joint optimization frameworks to improve pose estimation accuracy.
• A Neural Network Acceleration of Iterative Methods for Nonlinear Schrödinger Eigenvalue Problems that demonstrates significant speed-up over classical solvers.
• A Stable Iterative Solvers for Ill-conditioned Linear Systems approach that ensures stability and prevents divergence in Krylov subspace iterative solution methods.