Publication: On evaluating higher-order derivatives of the QR decomposition of tall matrices with full column rank in forward and reverse mode algorithmic differentiation
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On evaluating higher-order derivatives of the QR decomposition of tall matrices with full column rank in forward and reverse mode algorithmic differentiation

- Article in a journal -
 

Author(s)
Sebastian F. Walter , Lutz Lehmann , René Lamour

Published in
Optimization Methods and Software

Year
2012

Abstract
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.

AD Theory and Techniques
Higher Order, Taylor Arithmetic

BibTeX
@ARTICLE{
         Walter2012Oeh,
       author = "Walter, Sebastian F. and Lehmann, Lutz and Lamour, Ren\'{e}",
       title = "On evaluating higher-order derivatives of the {QR} decomposition of tall matrices with
         full column rank in forward and reverse mode algorithmic differentiation",
       journal = "Optimization Methods and Software",
       volume = "27",
       number = "2",
       pages = "391--403",
       year = "2012",
       doi = "10.1080/10556788.2011.610454",
       url = "http://www.tandfonline.com/doi/abs/10.1080/10556788.2011.610454",
       eprint = "http://www.tandfonline.com/doi/pdf/10.1080/10556788.2011.610454",
       abstract = "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.",
       ad_theotech = "Higher Order, Taylor Arithmetic"
}


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