On evaluating higher-order derivatives of the QR decomposition of tall matrices with full column rank in forward and reverse mode algorithmic differentiation
We address the task of higher-order derivative evaluation of computer programs that contain QR decompositions of tall matrices with full column rank. The approach is a combination of univariate Taylor polynomial arithmetic and matrix calculus in the (combined) forward/reverse mode of algorithmic differentiation (AD). Explicit algorithms are derived and presented in an accessible form.
univariate taylor polynomial arithmetic automatic differentiation null space