A Short Proof for Gap Independence of Simultaneous Iteration
Edo Liberty
TL;DR
This paper presents a concise, self-contained proof demonstrating that the simultaneous iterations algorithm's effectiveness in finding the top singular space does not depend on the spectral gap, simplifying previous complex proofs.
Contribution
It offers a very short, accessible proof of the spectral gap independence property for the simultaneous iterations algorithm, improving understanding and clarity.
Findings
Proof is terse but self-contained
Spectral gap independence of the algorithm confirmed
Accessible to linear algebra practitioners
Abstract
This note provides a very short proof of a spectral gap independent property of the simultaneous iterations algorithm for finding the top singular space of a matrix. See Rokhlin-Szlam-Tygert-2009, Halko-Martinsson-Tropp-2011 and Musco-Musco-2015. The proof is terse but completely self contained and should be accessible to the linear algebra savvy reader.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Optimization Algorithms Research · Sparse and Compressive Sensing Techniques