Exponential convergence of Sobolev gradient descent for a class of nonlinear eigenproblems

DOI10.4310/CMS.2022.v20.n2.a4zbMath1483.35143arXiv1912.02135OpenAlexW2992101403WikidataQ115481142 ScholiaQ115481142MaRDI QIDQ2076202

Zi-Yun Zhang

Publication date: 16 February 2022

Published in: Communications in Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.02135

zbMATH Keywords

Schrödinger equationŁojasiewicz inequalitySobolev gradient descentGross-Pitaevskii eigenprobleminfinite dimensional Hilbert manifold

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Boundary value problems for second-order elliptic equations (35J25) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Theoretical approximation in context of PDEs (35A35) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Semilinear elliptic equations (35J61)

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Energy-adaptive Riemannian optimization on the Stiefel manifold ⋮ An overview of \textit{a posteriori} error estimation and post-processing methods for nonlinear eigenvalue problems ⋮ On the Convergence of Sobolev Gradient Flow for the Gross–Pitaevskii Eigenvalue Problem ⋮ The dependency of spectral gaps on the convergence of the inverse iteration for a nonlinear eigenvector problem ⋮ On Optimal Convergence Rates for Discrete Minimizers of the Gross–Pitaevskii Energy in Localized Orthogonal Decomposition Spaces

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