Grassmannian packings: Trust-region stochastic tuning for matrix incoherence

TL;DR

This paper introduces a new numerical method called TRSTMI for constructing low coherence matrices, demonstrating its effectiveness on large matrices through parallelized experiments and proposing new conjectures on optimal complex matrices.

Contribution

The paper presents TRSTMI, a novel stochastic optimization procedure for matrix incoherence, with experimental validation and new conjectures on optimal complex matrices.

Findings

TRSTMI outperforms existing methods on large matrices

Parallelized implementation enhances computational efficiency

Experimental results motivate new conjectures on optimal matrices

Abstract

We provide a new numerical procedure for constructing low coherence matrices, Trust-Region Stochastic Tuning for Matrix Incoherence (TRSTMI) and detail the results of experiments with a CPU/GPU parallelized implementation of this method. These trials suggest the superiority of this approach over other existing methods when the size of the matrix is large. We also present new conjectures on optimal complex matrices motivated and guided by the experimental results.