Showing math.NAShow all
3 papers · 1 filter
math.NA2025
Faithful-Newton Framework: Bridging Inner and Outer Solvers for Enhanced Optimization
Alexander Lim, Fred Roosta
Newton-type methods enjoy fast local convergence and strong empirical performance, but achieving global guarantees comparable to first-order methods remains challenging. Even for s…
math.NA2025
Obtaining Pseudo-inverse Solutions With MINRES
Yang Liu, Andre Milzarek, Fred Roosta
The celebrated minimum residual method (MINRES), proposed in the seminal paper of Paige and Saunders, has seen great success and widespread use in solving Hermitian (and complex-sy…
math.NA2025
Conjugate Direction Methods Under Inconsistent Systems
Alexander Lim, Yang Liu, Fred Roosta
Since the development of the conjugate gradient (CG) method in 1952 by Hestenes and Stiefel, CG, has become an indispensable tool in computational mathematics for solving positive…