On the Upper Bounds for the Matrix Spectral Norm

• URL: http://arxiv.org/abs/2506.15660v1
• Date: Wed, 18 Jun 2025 17:39:03 GMT
• Title: On the Upper Bounds for the Matrix Spectral Norm
• Authors: Alexey Naumov, Maxim Rakhuba, Denis Ryapolov, Sergey Samsonov,
• Abstract summary: We propose a new Counterbalance estimator that provides upper bounds on the norm and derive probabilistic guarantees on its underestimation.<n>Compared to standard approaches such as the power method, the proposed estimator produces significantly tighter upper bounds in both synthetic and real-world settings.
• Score: 4.773232329447336
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider the problem of estimating the spectral norm of a matrix using only matrix-vector products. We propose a new Counterbalance estimator that provides upper bounds on the norm and derive probabilistic guarantees on its underestimation. Compared to standard approaches such as the power method, the proposed estimator produces significantly tighter upper bounds in both synthetic and real-world settings. Our method is especially effective for matrices with fast-decaying spectra, such as those arising in deep learning and inverse problems.

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