Summary of convergence and cost of the QR iteration

Unsymmetric case

• Upper Hessenberg: $O(n^3)$
• QR iteration step: $O(n^2)$
• QR iteration: $O(n_{\text{quad}}{n}^3)$
• Convergence: $\epsilon \to O({\epsilon }^2)$

Symmetric case

• Upper Hessenberg: $O(n^3)$
• QR iteration step: $O(n)$
• QR iteration: $O(n_{\text{cub}}{n}^2)$
• Convergence: $\epsilon \to O({\epsilon }^3)$