I.4.2: Convergence rate

The product form of the derivative of the algorithmic map for coordinate descent is $$\mathcal{M}(x)=\left[I-\frac{e_pe_p'\mathcal{D}^2f(x)} {e_p'\mathcal{D}^2f(x)e_p}\right] \times\cdots\times \left[I-\frac{e_1e_1'\mathcal{D}^2f(x)}{e_1'\mathcal{D}^2f(x)e_1}\right],$$ where the $e_s$ are unit vectors (all elements zero, except for element $s$, which is equal to one).