A Survey on Variational Characterizations for Nonlinear Eigenvalue Problems
Electronic transactions on numerical analysis(2021)
摘要
Variational principles are very powerful tools when studying self-adjoint linear operators on a Hilbert space H. Bounds for eigenvalues, comparison theorems, interlacing results, and monotonicity of eigenvalues can be proved easily with these characterizations, to name just a few. In this paper we consider generalizations of these principles to families of linear, self-adjoint operators depending continuously on a scalar in a real interval.
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关键词
nonlinear eigenvalue problem,variational characterization,iterative projection methods,AMLS,quantum dots,viscoelastic damping,total least-squares problems,fluid-solid interaction
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