Exponential convergence of Sobolev gradient descent for a class of nonlinear eigenproblems.
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...oncept of preconditioning for Riemannian optimization problems seems not to have been explored much in the mathematical literature, except in some specific models and preconditioners (see for instance [7,67] for the Gross-Pitaevskii model), and a deeper analysis of this would be interesting. In particular, this is necessary to extend the convergence theory presented in this paper to infinite-dimensional s...
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"Exponential convergence of Sobolev ..." refers background in this paper
...It is well known that the Anderson localization [3] is present in this setting....
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"Exponential convergence of Sobolev ..." refers background in this paper
..., u [2] h is the componentwise squared vector of uh....
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...The linearized operator Au,h now has a matrix representation in RN×N : Au,h = −Lh + diag{Vh + βu([2]) h },...
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...It has long been studied both in experiments [2] and in numerical analysis [8, 16, 22, 26]....
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