A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.
Sato, Riemannian Optimization and Its Applications
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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.
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A second-order method landing on the Stiefel manifold via Newton$\unicode{x2013}$Schulz iteration
A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.
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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.
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