On the growth factor upper bound for Aasen's algorithm
For numerical linear algebra researchers, this provides a refined theoretical guarantee on stability of Aasen's algorithm.
The paper derives a tighter upper bound for the growth factor in Aasen's algorithm for symmetric indefinite matrices, showing it is significantly smaller than the previous bound by Higham, and proves the bound is not tight for dimensions ≥6.
Aasen's algorithm factorizes a symmetric indefinite matrix $A$ as $A = P^TLTL^TP$, where $P$ is a permutation matrix, $L$ is unit lower triangular with its first column being the first column of the identity matrix, and $T$ is tridiagonal. In this note, we provide a growth factor upper bound for Aasen's algorithm which is much smaller than that given by Higham. We also show that the upper bound we have given is not tight when the matrix dimension is greater than or equal to $6$.