Tootfinder

Sharp error bounds for approximate eigenvalues and singular values from subspace methods
Irina-Beatrice Haas, Yuji Nakatsukasa
https://arxiv.org/abs/2506.01207

Sharp error bounds for approximate eigenvalues and singular values from subspace methods
Subspace methods are commonly used for finding approximate eigenvalues and singular values of large-scale matrices. Once a subspace is found, the Rayleigh-Ritz method (for symmetric eigenvalue problems) and Petrov-Galerkin projection (for singular values) are the de facto method for extraction of eigenvalues and singular values. In this work we derive quadratic error bounds for approximate eigenvalues obtained via the Rayleigh-Ritz process. Our bounds take advantage of the fact that extremal ei…

Beating the Logarithmic Barrier for the Subadditive Maximin Share Problem
Masoud Seddighin, Saeed Seddighin
https://arxiv.org/abs/2506.05613 https://

Beating the Logarithmic Barrier for the Subadditive Maximin Share Problem
We study the problem of fair allocation of indivisible goods for subadditive agents. While constant-\textsf{MMS} bounds have been given for additive and fractionally subadditive agents, the best existential bound for the case of subadditive agents is $1/O(\log n \log \log n)$. In this work, we improve this bound to a $1/O((\log \log n)^2)$-\textsf{MMS} guarantee. To this end, we introduce new matching techniques and rounding methods for subadditive valuations that we believe are of independent …

Beating joint quantum estimation limits with stepwise multiparameter metrology
Chiranjib Mukhopadhyay, Abolfazl Bayat, Victor Montenegro, Matteo G. A. Paris
https://arxiv.org/abs/2506.06075

Beating joint quantum estimation limits with stepwise multiparameter metrology
Conventional multiparameter quantum sensing relies on joint estimation, but this approach faces two key limitations: theoretical bounds may be unattainable due to measurement incompatibility, and sensing may fail due to parameter interdependencies. We propose stepwise estimation and identify regimes where it outperforms joint estimation. For multiple quantum sensors, this scheme achieves far lower error bounds than joint estimation. With many-body probes, stepwise sensing retains a quantum-enha…