Speaker
Description
In this talk, we introduce a unified framework for nonlinear Krylov subspace methods (nlKrylov ) to solve systems of nonlinear equations. Building on the recent development of nlTGCR as well as earlier work on classical GCR-like linear Krylov solvers such as GMRESR, we generalize these approaches to non-linear problems via nested algorithmic structures. We establish connections of nlKrylov methods to other existing nonlinear methods such as quasi-Newton and subspace projection methods. Our theory is completed by rigorous convergence results for problems with both nonsingular and singular Jacobian. The framework is further extended to matrix-valued rootfinding problems using global nonlinear Krylov approaches. Extensive numerical experiments validate the theoretical insights and demonstrate the robustness and efficiency of our proposed algorithms.