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math.CO2022
On Eigenvalue Gaps of Integer Matrices
Aaron Abrams, Zeph Landau, Jamie Pommersheim +1
Given an matrix with integer entries in the range , how close can two of its distinct eigenvalues be? The best previously known examples have a minimum gap of $…
math.NA2022
Global Convergence of Hessenberg Shifted QR II: Numerical Stability
Jess Banks, Jorge Garza-Vargas, Nikhil Srivastava
We develop a framework for proving rapid convergence of shifted QR algorithms which use Ritz values as shifts, in finite arithmetic. Our key contribution is a dichotomy result whic…
math.NA2022★ 1 cited
Global Convergence of Hessenberg Shifted QR III: Approximate Ritz Values via Shifted Inverse Iteration
Jess Banks, Jorge Garza-Vargas, Nikhil Srivastava
We give a self-contained randomized algorithm based on shifted inverse iteration which provably computes the eigenvalues of an arbitrary matrix up to b…