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

We address the task of higher-order derivative evaluation of computer programs that contain QR decompositions and real symmetric eigenvalue decompositions. 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. The approach is illustrated via examples.

preprint2010arXivOpen access
Sebastian F. WalterLutz LehmannRené Lamour
math.NA
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Open access3 authors1 topic
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Citations: 0Reviews: 0Saves: 0Code: not linkedDataset: not linkedInstitutions: 0

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Sebastian F. WalterLutz LehmannRené Lamour

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