Exact low-dimensional reformulations for regularized spectral approximation

Shengxiang Deng; Xudong Li; Yangjing Zhang

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arXiv · 2608.27052

Exact low-dimensional reformulations for regularized spectral approximation

Shengxiang Deng·Xudong Li·Yangjing Zhang

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Abstract

We study exact low-dimensional reformulations for a regularized spectral approximation problem and its weighted variant. In the unweighted setting, weak-majorization monotonicity of the fidelity term enables an exact reformulation over singular values. In the weighted setting, we establish such a reformulation under compatibility and simultaneous diagonalization conditions. We further show, via a counterexample, that this exact reformulation can fail in the absence of simultaneous diagonalization.

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Shengxiang Deng, Xudong Li, Yangjing Zhang. 2026-08-27. Exact low-dimensional reformulations for regularized spectral approximation. https://arxiv.org/abs/2608.27052

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