Table 1 Comparison of various distributed QR factorization algorithms
From: Distributed Gram-Schmidt orthogonalization with simultaneous elements refinement
Total number of | Total amount of | Local memory | |
|---|---|---|---|
sent messages | data (real numbers) | requirements | |
per node | |||
DS-CGS | N·I (d) | \(N\cdot I^{(d)} \cdot \frac {m^{2}+5m}{2}\) | O(mn/N + m 2) |
AC-CGS | \(N \cdot I^{(s)}\cdot \frac {(m+1)m}{2}\) | \(N \cdot I^{(s)} \cdot \frac {(m+1)m}{2}\) | O(mn/N + m 2) |
G-CGS | N·R·(2m−1) | \(N \cdot R \cdot \frac {m^{2}+5m-2}{2}\) | O(nm/N) |
G-MGS | N·R·(2m−1) | \(N \cdot R \cdot \frac {m^{2}+5m-2}{2}\) | O(nm/N) |