Numerical Stability of Tangents and Adjoints of Implicit Functions
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We investigate errors in tangents and adjoints of implicit functions resulting from errors in the primal solution due to approximations computed by a numerical solver. Adjoints of systems of linear equations turn out to be unconditionally numerically stable. Tangents of systems of linear equations can become instable as well as both tangents and adjoints of systems of nonlinear equations, which extends to optima of convex unconstrained objectives. Sufficient conditions for numerical stability are derived.
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