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math.NA2026
On the exponential rate of the condition number of Fourier submatrices and Vandermonde matrices
Rikhav Shah, John Urschel
The discrete Fourier transform matrix is one of the most important matrices in linear algebra, and submatrices of it arise in a variety of applications. Though the discrete Fourier…
math.NA2026
The largest 5th pivot may be the root of a 61st degree polynomial
James Chen, Alan Edelman, John Urschel
This paper introduces a number of new techniques in the study of the famous question from numerical linear algebra: what is the largest possible growth factor when performing Gauss…
math.NA2024
Estimating the numerical range with a Krylov subspace
Cecilia Chen, John Urschel
Krylov subspace methods are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we study the approximation quality that a Krylov subspac…