Table 2 Number of reads and writes at each step (in bytes)
From: A MapReduce-based Adjoint method for preventing brain disease
| Â | Cholesky (Bytes) | Indirect TSQR (bytes) | Direct TSQR (bytes) | Householder QR (bytes) | MR-AM (bytes) |
|---|---|---|---|---|---|
\(R_{1}^{m}\) | 8mn + Km | 8mn + Km | 8mn + Km | 8mn + Km | Kmn + (m − 1)(n − 1) |
\(W_{1}^{m}\) | 8m1n2 + 8m1n | 8m1n2 + 8m1n | \(8mn + 8m_{1} n^{2} + Km + 64m_{1}\) | 8mn + Km | Kmn + 8mn |
\(R_{1}^{r}\) | 8m1n2 + 8m1n | 8m1n2 + 8m1n | 0 | 0 | kmn + 8mn |
\(W_{1}^{r}\) | 8n2 + 8n | 8r1n2 + 8r1n | 0 | 0 | 8 k + 8 k |
\(R_{2}^{m}\) | 8n2 + 8n | 8r1n2 + 8r1n | 8m1n2 + Km1 | 8mn + Km | – |
\(W_{2}^{m}\) | 8n2 + 8n | 8r1n2 + 8r1n | 8m1n2 + Km1 | 16m1 | – |
\(R_{2}^{r}\) | 8n2 + 8n | 8r1n2 + 8r1n | 8m1n2 + Km1 | 0 | – |
\(W_{2}^{r}\) | 8n2 + 8n | 8n2 + 8n | \(8m_{1} n^{2} + 32m_{1} + 8n^{2} + 8n\) | 0 | – |
\(R_{3}^{m}\) | \(8mn + Km + m_{3} \left( {8n^{2} + 8n} \right)\) | \(8mn + Km + m_{3} \left( {8n^{2} + 8n} \right)\) | \(8mn + Km + m_{3} \left( {8m_{1} n^{2} + 64m_{1} }\right)\) | – | – |
\(W_{3}^{m}\) | 8mn + Km | 8mn + Km | 8mn + Km | – | – |
\(R_{3}^{r}\) | 0 | 0 | 0 | – | – |
\(W_{3}^{r}\) | 0 | 0 | 0 | – | – |