Author

Ekene Ezeunala

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Preprint Sep 2026

Rank-One Matrix Discrepancy and Algorithmic Kadison--Singer

We give a deterministic polynomial-time algorithm that, given rational Hermitian matrices $H_1,\dots,H_N$ of rank at most one, finds signs $s\in\{\pm1\}^N$ with $\|\sum_i s_i H_i\|\le 13\|\sum_i H_i^2\|^{1/2}$. As a corollary, for vectors $v_i$ with $\sum_i v_iv_i^*=I$ and $\|v_i\|^2\le\delta$, the signs yield a partit...

Ekene Ezeunala, Hao-Tian Jiang · 2 citations · ⚡1

Preprint Sep 2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benef...

Ekene Ezeunala, Agastya Vibhuti Jha, Hao-Tian Jiang · 0 citations