Sequence of operations for the ℋ-Cholesky factorization of A: |
O1 : A1,1 | $\begin{array}{}
= {L_{1,1}}L_{1,1}^T
\end{array}$ |
O2 : L2,1 | $\begin{array}{}
{\rm{: = }}{A_{2,1}}L_{1,1}^{ - T}
\end{array}$ |
O3 : A2,2 | $\begin{array}{}
{\rm{: = }}{A_{2,2}} - {L_{2,1}} \cdot L_{2,1}^T
\end{array}$ |
O4 : A2,2 | $\begin{array}{}
{\rm{ = }}{L_{2,2}}L_{2,2}^T
\end{array}$ |
O5 : L3:4, 1:2 | $\begin{array}{}
{\rm{: = }}{A_{3:4,1:2}}L_{1:2,1:2}^{ - T}
\end{array}$ |
O6 : A3:4, 3:4 | $\begin{array}{}
{\rm{: = }}{A_{3:4,3:4}} - {L_{3:4,1:2}} \cdot L_{3:4,1:2}^T
\end{array}$ |
O7 : A3, 3 | $\begin{array}{}
= {L_{3,3}}L_{3,3}^T
\end{array}$ |
O8 : L4, 3 | $\begin{array}{}
{\rm{: = }}{A_{4,3}}L_{3,3}^{ - T}
\end{array}$ |
O9 : A4, 4 | $\begin{array}{}
{\rm{: = }}{A_{4,4}} - {L_{4,3}} \cdot L_{4,3}^T
\end{array}$ |
O10 : A4, 4 | $\begin{array}{}
= {L_{4,4}}L_{4,4}^T
\end{array}$ |