Adjoint differentiation for generic matrix functions

Andrei Goloubentsev, Dmitri Goloubentsev and Evgeny Lakshtanov

Journal of Computational Finance

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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