Table 1 A comparison of C-to-IO ratios for inverting an N × N matrix using the Richardson methoda
From: I/O-efficient iterative matrix inversion with photonic integrated circuits
CPU | TPU | PSP | PIP | |
|---|---|---|---|---|
Input data size | \(2{N}^{2}\cdot P\) | \({N}^{2}\cdot P\) | \({N}^{2}\cdot P\) | \(N\) |
Output data size | \({N}^{2}\cdot P\) | \({N}^{2}\cdot P\) | \({N}^{2}\cdot P\) | \({N}^{2}\) |
Memory access countsb | \(3{N}^{2}\cdot P\) | \({N}^{2}\cdot (2P+1)\) | \({N}^{2}\cdot (2P+1)\) | \(2{N}^{2}+N\) |
Number of operationsc | \({N}^{3}\cdot P\) | \({N}^{3}\cdot P\) | \({N}^{3}\cdot P\) | \({N}^{3}\cdot P\) |
C-to-IO ratio | \(N/3\) | \({NP}/(2P+1)\) | \({NP}/(2P+1)\) | \({N}^{3}P/(2{N}^{2}+N)\) |
