Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Second EditionAlgorithmic, or automatic, differentiation (AD) is a growing area of theoretical research and software development concerned with the accurate and efficient evaluation of derivatives for function evaluations given as computer programs. The resulting derivative values are useful for all scientific computations that are based on linear, quadratic, or higher order approximations to nonlinear scalar or vector functions. This second edition covers recent developments in applications and theory, including an elegant NP completeness argument and an introduction to scarcity. There is also added material on checkpointing and iterative differentiation. To improve readability the more detailed analysis of memory and complexity bounds has been relegated to separate, optional chapters. The book consists of: a stand-alone introduction to the fundamentals of AD and its software; a thorough treatment of methods for sparse problems; and final chapters on program-reversal schedules, higher derivatives, nonsmooth problems and iterative processes. |
Contents
OT105_ch1 | 1 |
OT105_ch2 | 15 |
OT105_ch3 | 31 |
OT105_ch4 | 61 |
OT105_ch5 | 91 |
OT105_ch6 | 107 |
OT105_ch7 | 145 |
OT105_ch8 | 161 |
OT105_ch10 | 211 |
OT105_ch11 | 245 |
OT105_ch12 | 261 |
OT105_ch13 | 299 |
OT105_ch14 | 335 |
OT105_ch15 | 367 |
OT105_bm | 397 |
OT105_ch9 | 185 |
Other editions - View all
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation Andreas Griewank No preview available - 1987 |
Common terms and phrases
adouble algorithm apply argument arithmetic operations assume assumption bound calculation call tree chain rule Chapter checkpointing column complexity components compression computational graph consider control flow graph corresponding cost defined denote dependent difference quotients differentiation directional derivatives domain edges elemental functions elimination equation evaluation procedure exactly example Exercise F(zk Fixed Point Iteration floating point forward and reverse forward mode forward sweep function F gradient Hence Hessian implementation incremental independent variables intermediate iteration Jacobian Laurent Lemma linear Lipschitz continuous listed in Table loop Markowitz matrix maximal minimal multiplications Newton's method nonincremental nonlinear nonzero obtain OpenMP operations count operator overloading optimal overwriting polynomial problem propagation Proposition recurrence reduce respect result return sweep reversal schedule reverse mode runtime scalar second-order adjoint sparse sparsity tangent tape Taylor coefficients Taylor polynomials tensor univariate values vector vertices Vi-n yields zero