5 papers · 1 filter
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…
On the Frobenius norm of the inverse of a non-negative matrix
Elsa Frankel, John Urschel
We prove a new lower bound for the Frobenius norm of the inverse of an non-negative matrix. This bound is only a modest improvement over previous results, but is sufficient for ful…
On a perturbation analysis of Higham squared maximum Gaussian elimination growth matrices
Alan Edelman, John Urschel, Bowen Zhu
Gaussian elimination is the most popular technique for solving a dense linear system. Large errors in this procedure can occur in floating point arithmetic when the matrix's growth…
Average Nodal Count and the Nodal Count Condition for Graphs
Lior Alon, John Urschel
The nodal edge count of an eigenvector of the Laplacian of a graph is the number of edges on which it changes sign. This quantity extends to any real symmetric matrix s…
Recovering a Magnitude-Symmetric Matrix from its Principal Minors
Victor-Emmanuel Brunel, John Urschel
We consider the inverse problem of finding a magnitude-symmetric matrix (matrix with opposing off-diagonal entries equal in magnitude) with a prescribed set of principal minors. Th…