Automatic implicit function theorem
New technique can improve use of adjoint algorithmic differentiation in calibration problems
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Dmitri Goloubentsev, Evgeny Lakshtanov and Vladimir Piterbarg explain in mathematical terms, and demonstrate using a simple example, how the automatic implicit function theorem, a special version of the implicit function theorem, enables fully automated differentiation of exact-fit calibration routines. They show that the automatic implicit function theorem gives an approximate solution to the nearly exact calibration problems typical in practice, for which
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