Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Second Edition
This title is a comprehensive treatment of algorithmic, or automatic, differentiation. The second edition covers recent developments in applications and theory, including an elegant NP completeness argument and an introduction to scarcity.
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adouble algorithm apply argument arithmetic operations assumption bound calculation chain rule Chapter checkpointing column complexity components compression computational graph consider convergence corresponding cost deﬁned Deﬁnition dependent difference quotients differentiation diﬁerentiation directional derivatives domain edges efﬁciency elemental functions elimination equation evaluation procedure example Exercise ﬁnal ﬁnd ﬁnite ﬁrst ﬁxed ﬂoating point ﬂow forward and reverse forward mode forward sweep function F gradient Hence Hessian implementation incidence graph incremental independent variables intermediate iteration Jacobian Laurent linear Lipschitz continuous listed in Table loop Markowitz matrix maximal memory methods minimal multiplications nonincremental nonlinear nonzero obtain OpenMP operations count operator overloading optimal overwriting partial polynomial preprocessor problem propagation Proposition recurrence reduce requires respect result return sweep reverse mode reverse sweep runtime scalar Schur complement second-order adjoint signiﬁcant sparse sparsity speciﬁcally tangent tape Taylor coefﬁcients Taylor polynomials Taylor series tensor univariate values vector vertices yields zero