| Abstract |
This final talk illustrates the scope and utility of the auxiliary-space viewpoint through several important classes of numerical methods. The framework applies to a broad range of advanced iterative methods, including subspace correction methods, Hiptmair--Xu preconditioners, saddle point solvers, and iterative substructuring methods.
Through these applications, we show how apparently different methods can be understood within a common structure: each may be interpreted as an elementary iteration on a suitably enlarged space. This perspective clarifies relationships among existing algorithms and suggests new ways to design efficient solvers. We conclude by discussing how this viewpoint may inform the development of numerical methods for problems arising in machine learning, where complexity is often shifted from the optimization procedure to the underlying representation. |
