1 citations · 1 across the 5 of their papers we have counts for
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Numerical Instability of Algebraic Rootfinding Methods
Emil Graf, Alex Townsend
We demonstrate that the most popular variants of all common algebraic multidimensional rootfinding algorithms are unstable by analyzing the conditioning of subproblems that are con…
How to reveal the rank of a matrix?
Anil Damle, Silke Glas, Alex Townsend +1
We study algorithms called rank-revealers that reveal a matrix's rank structure. Such algorithms form a fundamental component in matrix compression, singular value estimation, and…
Avoiding discretization issues for nonlinear eigenvalue problems
Matthew J. Colbrook, Alex Townsend
The first step when solving an infinite-dimensional eigenvalue problem is often to discretize it. We show that one must be extremely careful when discretizing nonlinear eigenvalue…
Leveraging the Hankel norm approximation and block-AAA algorithms in reduced order modeling
Annan Yu, Alex Townsend
Large-scale linear, time-invariant (LTI) dynamical systems are widely used to characterize complicated physical phenomena. We propose a two-stage algorithm to reduce the order of a…