4 papers · 1 filter
Sampling Pfaffian point processes and the symplectic Arnoldi method
Alan Edelman, Sungwoo Jeong, Simeon Schaub
We present an exact sampling algorithm for Pfaffian point processes based on a skew-symmetric analogue of the Cholesky factorization. This algorithm enables efficient sampling of a…
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…
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…
A New Upper Bound For the Growth Factor in Gaussian Elimination with Complete Pivoting
Ankit Bisain, Alan Edelman, John Urschel
The growth factor in Gaussian elimination measures how large the entries of an LU factorization can be relative to the entries of the original matrix. It is a key parameter in erro…