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- W4313442954 abstract "We consider a class of eigenvector-dependent nonlinear eigenvalue problems (NEPv) without the unitary invariance property. Those NEPv commonly arise as the first-order optimality conditions of a particular type of optimization problems over the Stiefel manifold, and previously, special cases have been studied in the literature. Two necessary conditions, a definiteness condition and a rank-preserving condition, on an eigenbasis matrix of the NEPv that is a global optimizer of the associated problem optimization are revealed, where the definiteness condition has been known for the special cases previously investigated. We show that, locally close to the eigenbasis matrix satisfying both necessary conditions, the NEPv can be reformulated as a unitarily invariant NEPv, the so-called aligned NEPv, through a basis alignment operation -- in other words, the NEPv is locally unitarily invariantizable. Numerically, the NEPv is naturally solved by an SCF-type iteration. By exploiting the differentiability of the coefficient matrix of the aligned NEPv, we establish a closed-form local convergence rate for the SCF-type iteration and analyze its level-shifted variant. Numerical experiments confirm our theoretical results." @default.
- W4313442954 created "2023-01-06" @default.
- W4313442954 creator A5011252539 @default.
- W4313442954 creator A5086939495 @default.
- W4313442954 date "2022-12-28" @default.
- W4313442954 modified "2023-10-18" @default.
- W4313442954 title "Convergence of SCF for Locally Unitarily Invariantizable NEPv" @default.
- W4313442954 doi "https://doi.org/10.48550/arxiv.2212.14098" @default.
- W4313442954 hasPublicationYear "2022" @default.
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