The field of numerical methods for partial differential equations (PDEs) and linear algebra is rapidly advancing, with a focus on developing efficient and accurate methods for solving complex problems. Recent research has highlighted the importance of preconditioning techniques, such as operator preconditioning and multigrid solvers, for improving the convergence of iterative methods. Additionally, there is a growing interest in the development of novel methods, such as the DualTPD method and the Waveholtz iteration, for solving nonlinear PDEs and Helmholtz equations. The use of rational filter methods, such as the ParaSLRF method, is also becoming increasingly popular for solving large-scale eigenvalue problems. Furthermore, researchers are exploring the application of optimal control techniques to minimize residuals in ODE integration and to improve the accuracy of numerical solutions. Noteworthy papers in this area include the proposal of a Novel Preconditioning Framework for Solving Nonlinear PDEs, which introduces a new method for solving nonlinear PDEs using Fenchel-Rockafellar duality and transformed primal-dual techniques. Another notable paper is the ParaSLRF method, which presents a parallel implementation of the Shifted Laplace Rational Filter method for solving large-scale eigenvalue problems, showing excellent parallel efficiency and load balance.