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Griewank A. — Evaluating derivatives: principles and techniques of algorithmic differentiation
Griewank A. — Evaluating derivatives: principles and techniques of algorithmic differentiation

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Название: Evaluating derivatives: principles and techniques of algorithmic differentiation

Автор: Griewank A.

Аннотация:

Algorithmic, or automatic, differentiation (AD) is concerned with the accurate and efficient evaluation of derivatives for functions defined by computer programs. No truncation errors are incurred, and the resulting numerical derivative values can be used for all scientific computations that are based on linear, quadratic, or even higher order approximations to nonlinear scalar or vector functions. In particular, AD has been applied to optimization, parameter identification, equation solving, the numerical integration of differential equations, and combinations thereof. Apart from quantifying sensitivities numerically, AD techniques can also provide structural information, e.g., sparsity pattern and generic rank of Jacobian matrices.

This first comprehensive treatment of AD describes all chainrule-based techniques for evaluating derivatives of composite functions with particular emphasis on the reverse, or adjoint, mode. The corresponding complexity analysis shows that gradients are always relatively cheap, while the cost of evaluating Jacobian and Hessian matrices is found to be strongly dependent on problem structure and its efficient exploitation. Attempts to minimize operations count and/or memory requirement lead to hard combinatorial optimization problems in the case of Jacobians and a well-defined trade-off curve between spatial and temporal complexity for gradient evaluations.

The book is divided into three parts: a stand-alone introduction to the fundamentals of AD and its software, a thorough treatment of methods for sparse problems, and final chapters on higher derivatives, nonsmooth problems, and program reversal schedules. Each of the chapters concludes with examples and exercises suitable for students with a basic understanding of differential calculus, procedural programming, and numerical linear algebra.



Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 394

Добавлена в каталог: 03.03.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Activity analysis      111
Additive tasks      29
Addressing scheme &      26
ADIFOR      40 45 86 113 128 142 159 185 189 211
Adjoint as Lagrange multiplier      52
Adjoint complexity      84
Adjoint consistency      74
Adjoint gradient complexity      57
Adjoint higher order      238
Adjoint mode      8
Adjoint of adjoint      69 79
Adjoint of tangent      69 82
Adjoint operation      10 53
Adjoint pairs      55
Adjoint procedure      49
Adjoint second-order      83 107
Adjoint sensitivity equation      284
Adjoint Taylor exponential      233
Adjoint value      51
Adjoint variable      8
Adjoint, implicit      284
Adjoint, incremental      48
Adjoint, nonincremental      48 58
ADOL-C      112 225 233 312
Advancing      313
Algorithmic differentiation (AD)      1
Alias-safe      40 53
Aliasing      74
allocation      26
Approximants of Intermediates      221
Assignment, incremental      48 73
Assignment, iterative      71
Assignment, operator      100
Assignment, single      26 305
Average domain size      125
Back-elimination      170
Bough      313
Call tree      306
Chain rule      24
Chance constraint      253
Cheap gradient principle      60
Checkpointing      319
Chromatic number      140
Code preparation      210
Coleman — Verma partition      149
Coloring      140
Compatibility requirements      30
complexity      29—34
composition      223
Compressed tensor      152
Compression, column      139
Compression, combined      148
Compression, CPR      146
Compression, NR      146
Compression, row      139
Compression, simultaneous      152
Compression, two-sided      151
Consistency, adjoint      75
Consistency, derivative      28
Consistency, pattern      145
Contractive Preconditioning      289
Convergence rate      288
Copy-on-write      54
Cotangent      46
Cross-country      163
Curtis-Powell-Reid (CPR) seeding      140
Deactivation      101 291
Deinitializing      99
Derivative, addressing      41
Derivative, aliasing      41
Derivative, Cartesian      37
Derivative, directional      42 97 137
Derivative, discontinuous      252
Derivative, recurrence      291
Derivative, second      151
Difference quotient      137
Differentiable piecewise      261
Differential algebraic equation      247
Differential equation ordinary      243
Differentiation, algorithmic or automatic or computational      1
Differentiation, backward      46
Differentiation, generalized      264
Differentiation, reverse      46
Divided difference      see "Difference quotient"
Doublet      96
Dynamic programming      322
Edge-elimination      160
Edge-elimination rule      169
Elemental Differentiability      24
Elemental function      21
Elemental partials      22
Elemental Task Boundedness      33
Elimination, cross-country      167
Elimination, Gaussian      166
Elimination, rule      171
Elimination, sequence      180
Evaluation, graph      16
Evaluation, procedure      16
Evaluation, procedure, three-part      18
Evaluation, program      16
Evaluation, trace      5 16
Evolution      72 180 319
Extended Jacobian      22
Extended system      21
External memory      304
Feasible partition      150
Finite selection      261
Finite Slopes      281
Finite termination      172
Fixed point      298
Fortran calling sequence      113
Forward      37 161
forward compatibility      27
Forward incremental      173
Forward mode      6 7
Forward motion or sweep      49
Forward nonincremental      173
Forward overwriting      41
Forward propagation      127
Forward sparse      130
Front-elimination      171
Function addressing      71
Function allocation      26
Function composite      15 19
Function elemental      18 20
Function Heaviside      266
Function intermediate      20
Function kink      265
Function pole      267
Function reciprocal      23
Function rewriting      211
Function root      266
Function step      266
Funnel      188
Gaussian elimination      166
Generic rank      187
Gradient      see "Adjoint"
Gradient complexity      56
Gradient, higher order      233
Gradient, principle      60
Gradient, propagation      45
Gradient, reduced      52
Graph, bipartite      168
Graph, computational      333
Graph, quotient      184
hessian      121
Hessian cost ratio      155
Hessian graph      190
Hessian Lagrangian      133
Hessian, reduced width      155
IEEE arithmetic      266
Implementation, forward      98
Implementation, reverse      103
Implicit, adjoint      284
Implicit, tangent      284
Incremental, forward      173
Incremental, recursion      48
Incremental, reverse      173
Independent variable      see "Variable"
Index domain      123
Index range      124
Initialization function      21
Interaction binary      142
Interface contraction      185
intermediate      see "Variable"
Isolated Criticalities      267
Jacobian      121 161 201
Jacobian Regularity      283
Jacobian, extended      163
Jacobian, generalized      280
Jacobian, global      187
Jacobian, higher order      233
Jacobian, local      187
Jacobian, transpose      64
Jacobian-vector      39
Joint allocation      xviii
Karush — Kuhn — Tucker      52 284
Kink function      265
Laurent model      276
Laurent number      270
Levi-Civita number      256
Lifespan      56
Lighthouse example      253
Limited-Memory BFGS      89
Link, strong or weak      312
Local Jacobians and procedures      187
Locations      26
LU factorization      88
Markowitz heuristic      179
Matrix chaining      159 184
Matrix compression      135 139
Matrix reconstruction      153
Matrix seed      137
Matrix sparse      121
Matrix width      125
Matrix, Vandermonde      143
Memory location      26
Mode, forward      6 7
Mode, joint or split      312
Mode, reverse      8 103 104
Mode, selection      211
Mode, vector      42 55 109
Motion      309
Motion, cross-country      309
Multistep contractivity      292 296
Newsam — Ramsdell (NR) principle      139
Newsam — Ramsdell (NR) seeding      143
Newton method      256
Newton scenario      286
Newton step      195 286
Newton truncated      108
Nonincremental adjoint      58
Nonincremental adjoint, evaluation      48
Nonincremental form      80
Nonincremental forward      173
Nonincremental recursion      48
Nonincremental reverse      173
Nonlinear width or height      209
Odyssee      40 79 86 113 305 312 317
Overwrite      5 27 56
Pairs, compatible      308
Parallel chain      331
Parallel program      333
Partial separability      206
Partials, elemental      39
Partials, mixed      219
Partition Coleman — Verma      149
Path connectedness      124
Pathlength and pathvalue      168 184
Piecewise differentiability      261
Piggyback approach      286 300
Pole function      267
Polynomial core      23
Pre-value      53 76
Preaccumulation      159 185
Preconditioning      63 298
Preelimination      178
Preferred direction      251
Preprocessor      95 113
Problem preparation      209
Program, branch      266
Program, overloading      93
Program, transformation      91
Program, variable      5
Quotient convergence factor      289
Quotient graph      316
Randomly accessed memory      41
Range size      126
Rank-one example      199
Recalculation      304
Reciprocal      23
Recomputation      78
recording      313 315
Recursion, incremental or nonincremental      48
Reduced width      154
Reflexive      80
Regular Arc and Determinacy      279
Related task      29
Return motion or sweep      304
returning      312 313 315
Reversal      304 313
Reversal chain      320
Reversal joint      308 311
Reversal schedule      303—313 315—334
Reversal schedule, chain      328
Reversal schedule, parallel      330
Reversal Schedules      321
Reversal split      308 311
reverse      37 161
Reverse, compatibility      27
Reverse, differentiation      46
Reverse, implementation      103
Reverse, incremental      173
Reverse, mode      8 10
Reverse, motion or sweep      49
Reverse, nonincremental      173
Reverse, propagation      129
Reverse, sparse      132
Reverse, statement-level      188
Reverse, sweep      49
reversing      310
Root convergence factor      292
Root function      266
Runtime functional      31
Schedule, optimal      326
Schedule, reversal      315 328 330
Second derivatives      130 132
Seed, directions      37
Seed, matrix      137
Seeding, Curtis — Powell — Reid (CPR)      140
Seeding, Newsam — Ramsdell (NR)      155
Sensitivity, perturbation      51
Separability, argument      126 207
Separability, partial      131 202
Separability, value      206
Simplified recurrence      291
Source transformation      111
Sparsity      137
Sparsity, compression      137
Sparsity, dynamic      122
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