II.1.4.1: Rate of Convergence

Majorization is a special case of our results for augmentation previous theory, because $\mathcal{X}=\mathcal{Y}$ and because $y(x)=x$.

This implies that $\mathcal{D}_2(x,x)=0$ for all $x,$ and consequently $\mathcal{D}_{12}=-\mathcal{D}_{22}.$ Thus $\mathcal{M}(x)=-\mathcal{D}_{11}^{-1}\mathcal{D}_{12}^{\ }.$

Again, to some extent, finding a majorization function is an art. Many of the classical inequalities can be used (Cauchy-Schwarz, Jensen, H\"older, Young, AM-GM, and so on).