A Riemannian optimization method on fixed-rank matrix manifolds computes low-rank approximations to the solutions of parametrized systems, extending from linear to nonlinear cases with theoretical support for low-rank structure and preconditioning strategies.
Hiptmair, Operator preconditioning,Computers & Mathematics with Applications52no
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Low-rank solutions to a class of parametrized systems using Riemannian optimization
A Riemannian optimization method on fixed-rank matrix manifolds computes low-rank approximations to the solutions of parametrized systems, extending from linear to nonlinear cases with theoretical support for low-rank structure and preconditioning strategies.