Druinsky-Toledo¶
A Druinsky-Toledo matrix of order \(k\) is of the form
\[\begin{split}A_k = \begin{pmatrix} G_k & I_k \\ I_k & I_k \end{pmatrix},\end{split}\]
where
\[\begin{split}G_k = \begin{pmatrix} \text{diag}(d_0,d_1,\cdots,d_{n-3}) & \text{ones}(k-2,2) \\ \text{ones}(2,k-2) & \text{ones}(2,2) \end{pmatrix}\end{split}\]
Such a matrix is well-conditioned and achieves near the worst-case bound for element-growth with the “A” pivoting rule for Bunch-Kaufman factorizations
TODO: Longer description with a reference