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research article
Interlacing families III: Sharper restricted invertibility estimates
We use the method of interlacing families of polynomials to derive a simple proof of Bourgain and Tzafriri's Restricted Invertibility Principle, and then to sharpen the result in two ways. We show that the stable rank can be replaced by the Schatten 4-norm stable rank and that tighter bounds hold when the number of columns in the matrix under consideration does not greatly exceed its number of rows. Our bounds are derived from an analysis of the smallest zeros of Jacobi and associated Laguerre polynomials.
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Type
research article
Web of Science ID
WOS:000736140700008
Authors
Publication date
2022
Publisher
Published in
Volume
247
Start page
519
End page
546
Subjects
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
February 14, 2022