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Title: Adjoint differentiation for generic matrix functions
Author: Goloubentsev, Andrei
Goloubentsev, Dmitri
Lakshtanov, Evgeny
Issue Date: 13-Oct-2022
Publisher: Infopro Digital Services
Abstract: We derive a formula for the adjoint Ā of a square-matrix operation of the form f(A), where f is holomorphic in the neighborhood of each eigenvalue.We consider special cases such as the spectral decomposition A = UDU-1 and the spectrum cutoff f(A) = A+ for symmetric A. We then apply the formula to derive closed-form expressions in particular cases of interest to quantitative finance such as the “nearest correlation matrix” routine and regularized linear regression.
Peer review: yes
DOI: 10.21314/JCF.2022.024
ISSN: 1460-1559
Publisher Version:
Appears in Collections:CIDMA - Artigos
OGTCG - Artigos

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