5 citations · 11 across the 10 of their papers we have counts for
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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…
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…
Global Convergence of Hessenberg Shifted QR I: Exact Arithmetic
Jess Banks, Jorge Garza-Vargas, Nikhil Srivastava
Rapid convergence of the shifted QR algorithm on symmetric matrices was shown more than fifty years ago. Since then, despite significant interest and its practical relevance, an un…
Pseudospectral Shattering, the Sign Function, and Diagonalization in Nearly Matrix Multiplication Time
Jess Banks, Jorge Garza-Vargas, Archit Kulkarni +1
We exhibit a randomized algorithm which given a matrix with and , computes with high probability an invertible and diagonal …
The Lanczos Algorithm Under Few Iterations: Concentration and Location of the Output
Jorge Garza-Vargas, Archit Kulkarni
We study the Lanczos algorithm where the initial vector is sampled uniformly from . Let be an Hermitian matrix. We show that when run for few ite…