Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Second EditionThis 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. |
Contents
| 1 | |
| 15 | |
Fundamentals of Forward and Reverse | 31 |
Memory Issues and Complexity Bounds | 61 |
Repeating and Extending Reverse | 91 |
Implementation and Software | 107 |
Sparse Forward and Reverse | 145 |
Exploiting Sparsity by Compression | 161 |
Jacobian and Hessian Accumulation | 211 |
Observations on Efficiency | 245 |
Reversal Schedules and Checkpointing | 261 |
Taylor and Tensor Coefficients | 299 |
Differentiation without Differentiability | 335 |
Implicit and Iterative Differentiation | 367 |
Epilogue | 397 |
Going beyond Forward and Reverse | 185 |
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Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation Andreas Griewank No preview available - 1987 |
Common terms and phrases
accumulation additions adjoint analysis apply approach argument arithmetic assignment assume assumption bound calculation Chapter checkpointing coefficients column complexity components compression computational graph condition consider constant corresponding cost count defined dependent derivative determine difference differentiation directional discussed domain double edges elemental elimination equation evaluation procedure exactly example Exercise fact factor Figure forward function given gradient Hence Hessian implementation incremental independent initial intermediate iteration Jacobian linear listed matrix memory methods minimal multiplications nonlinear Note obtain occur once operations optimal original partial particular performed problem propagation Proposition recording reduce relation represent requires respect result reverse mode rule runtime separability simple solution statements steps structure sweep Table tangent task Taylor tool transformation tree values variables vector yields zero