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We address the task of higher-order derivative evaluation of computerprograms that contain QR decompositions and real symmetric eigenvaluedecompositions. The approach is a combination of univariate Taylor polynomialarithmetic and matrix calculus in the (combined) forward/reverse mode ofAlgorithmic Differentiation (AD). Explicit algorithms are derived and presentedin an accessible form. The approach is illustrated via examples.

Higher-order derivatives of the QR and of the real symmetric eigenvalue decomposition in forward and reverse mode algorithmic differentiation