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Adjoint differentiation for generic matrix functions

Author

Listed:
  • Andrei Goloubentsev
  • Dmitri Goloubentsev
  • Evgeny Lakshtanov

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.

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Handle: RePEc:rsk:journ0:7954858
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