# QR decomposition computational efficiency

I am struggling to find a reference for this: In terms of big Oh notation does anyone know of any expressions for the computational time taken by commonly used algorithms for QR decompositions?

Wikipedia says the complexity is $$O(n^3)$$ floating point multiplication operations when using Householder reflections.
The following table gives the number of operations in the $$k$$-th step of the QR-decomposition by the Householder transformation, assuming a square matrix with size $$n$$.
$$\begin{array}{c|c|} \text{Operation} & \text{Number of operations in kth step} \\ \hline \text{Multiplications} & 2(n-k+1)^2 \\ \hline \text{Additions} & (n-k+1)^2 + (n-k+1)(n-k)+2 \\ \hline \text{Divisions} & 1 \\ \hline \text{Square Root} & 1 \\ \hline \end{array}$$
Summing these numbers over the $$n-1$$ steps (for a square matrix of size $$n$$), the complexity of the algorithm (in terms of floating point multiplications) is given by
$$\frac{2}{3}n^3 + n^2+\frac{1}{3}n-2=O(n^3)$$