Author

David Persson

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Preprint Sep 2026

Hutch#: Optimal non-adaptive Frobenius norm estimation

The Girard--Hutchinson estimator provides an extremely simple randomized estimate of the Frobenius norm of a matrix $A$ that can only be accessed implicitly via matrix-vector products. In particular, if $\Omega$ is a random Gaussian matrix with $r = O(1/\varepsilon^2)$ columns, than $\frac{1}{r}\|A\Omega\|_F^2$ provide...

Tyler Chen, Diana Halikias, Christopher Musco et al. · 0 citations

Preprint Aug 2026

Optimal near-optimality bounds for the Lanczos method for matrix functions

Let $A$ be Hermitian positive definite and let $f_m$ denote the Lanczos approximation to $f(A)b$. We prove that if $f(z)$ or $f(z) / z$ is Stieltjes, then the $A^\alpha$-norm error of the Lanczos approximation is within a factor $\tfrac{1}{2}(\kappa(A)^{E/2} + \kappa(A)^{-E/2})$ of the the best possible Krylov Subspace...

Tyler Chen, David Persson · 0 citations