| Abstract |
A central goal of scientific computing is to develop accurate and efficient solvers for scientific problems, and this goal is often pursued through sophisticated numerical methods. In modern machine learning, by contrast, the basic optimization procedure is often comparatively simple, typically gradient descent and its variants, while much of the complexity is shifted to larger models.
This first talk introduces the main motivation of the talk series: to examine advanced iterative methods in scientific computing from a viewpoint inspired by this contrast. We begin with basic examples and preliminary concepts, including classical iterative methods, convergence of stationary iterations, and elementary schemes such as Jacobi, Gauss--Seidel, and Richardson iterations. These examples provide the foundation for the auxiliary-space perspective developed in the subsequent talks. |
