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| Rall L.B. — Automatic Differentiation: Techniques and Applications |
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| Предметный указатель |
A-format 116 117
Addressing, indirect 45
Airey, J. R. 152
ALPAK 154
ALTRAN 154
Approximation, improved 122
Approximation, initial 100 122
Arithmetic mean 116
Arithmetic mean, operation 4
Arithmetic mean, point 116
Arithmetic, interval 36 98 113
Assembly language 3
augment 2 88—90 154
Augmented gradient code list 92
Augmented gradient code list, gradient vector 89
Backward packing 33
Barton, D. 152
Basic representation 5
Basic representation, sequence 5
Bauer, F. L. 120
Bernoulli numbers 145 146
Bilinear operator 104
Bilinear operator, interval 115
Binary operation 5 15
Binomial coefficient 40
Cauchy problem 35 137
Cauchy problem, remainder term 36
Chain rule 11
Circle of convergence 35
Code list 4 5 27
Code list, augmented gradient 92
Code list, complete differential 38
Code list, complete gradient 92
Code list, compound 27
Code list, derivative 28
Code list, differential 28
Code list, function 5 27
Code list, gradient 92
Code list, Hessian 103
Code list, input 31
Code list, Jacobian 99
Code list, output 29 34
Code list, packed 29
Code list, simple 27
Codeable function 4
Coder 5 6 9 34 55 59
Codex 2 6 28 57—61 68 69 80 81 84 85 87 90 99 121 154
Coefficient, binomial 40
Coefficient, sensitivity 120
Coefficient, Taylor 35
Column vector 22 91 92
Compiler 3
Complete derivative code list 29
Complete derivative code list, differential code list 38
Complete derivative code list, gradient code list 92
composition 11
Compound code list 27
Compressor 81
Computation, parallel 8
Consistent norm 104
Constant 3 17
Constant, Lipschitz 118
Constant, literal 17
Constant, numerical 17
Constrained optimization 95
Constraint 94
Constraint, function 96
Continuation method 134
Continuity, Lipschitz 118
Convergence, circle of 35
Counter 59
Critical point 95
cube 124
Current label 45
Curve, homotopy 134
DATA 3 6
Data, base 6
Data, error 112 120
Davidenko's method 134 135
Davidenko, D. F. 134 135
Dependency tables 68
Derivative 9 91
Derivative code list 22
Derivative code list, code list, complete 29
Derivative code list, vector 22
Derivative, Frethet 23 91 100
Derivative, partial 9
Derivative, second 102
Derivative, semi-total 10 23
Destination node 40
Destination node of operation 60
DICTIONARY 27
Difference 99
Differentiable function 9
Differential 17 19 22 99
Differential code list 28
Differential code list, code list, complete 38
Differential code list, vector 22 120
Differential, relative 120
Differential, second 106
Differential, total 19
Differentiation 58
Differentiation, implicit 25
Differentiator 58 61
Directed graph 6
Directed graph, rounding 114
Division, symbolic 51
Element 60
Entry 27
Error term 140 142
Error, absolute 116 117
Error, data 112 120
Error, percentage 116 117
Error, relative 116 117
Error, roundoff 112
Error, truncation 112 140
Euclidean norm 2 3
Eulei — Maclaurin formula, interval 145
Evaluation 58
Explicit formula 25
Extension, interval 48 113
External label 45
Factorable function 5 13
Finite differences 97
Fixed-point problem 122
FORMAC 154
Formal partial derivative 10
Formula 5
FORmula TRANslation 3
Formula, explicit 25
Formula, simple 69
FORTRAN 3 8 34 38 55 58 60 81 84—87 89 114 143
Forward packing 32
Frehet derivative 23 91 100
Function code list 5 27
Function, codeable 4
Function, constraint 96
Function, differentiable 9
Function, factorable 5 13
Function, library 4
Function, power 47
Functional, linear 23 91
Geteaux derivative 23 91 100
Gradient 91
Gradient, code list 92
Gradient, code list, augmented 92
Gradient, code list, complete 92
Gradient, vector 92
Gradient, vector, augmented 89
Gragg, W. B. 127
| Graph, directed 6
Graph, Kantorovich 1 6 7
Gray, J. H. 55 57 130 153
Half-width 116
Hansen, E. 126
Harmonic mean 116
Harmonic mean, point 116
Hashing 90
Hassit, A. 58
Hessian code list 103
Hessian code list, matrix 102
Hessian code list, operator 102 105
Higher-level language 3
Homotopy curve 134
Homotopy curve, method 134
Homotopy curve, parameter 134
Implicit differentiation 25
Implicit differentiation, relationship 25
Improved approximation 122
Inclusion monotonicity 113
Indirect addressing 45
Initial approximation 100 122
Initial-value problem 35 137
Inner product 22
Input code list 31
INTE 2 141—151
Integration, numerical 138
Intermediate line 31 60
Intermediate line, storage 60
Internal label 45
Intersection property 142
interval 87 88
Interval arithmetic 36 98 113
Interval arithmetic, arithmetic package 113
Interval arithmetic, bilinear operator 115
Interval arithmetic, Euler — Maclaurin formula 145
Interval arithmetic, extension 48 113
Interval arithmetic, matrix 115
Interval arithmetic, remainder term 137
Interval arithmetic, Simpson's rule 141
Interval arithmetic, trapezoidal rule 141
Interval arithmetic, vector 115
Iteration 122
Iteration operator 122
Iteration, simple 122
Jacobian code list 99
Jacobian code list, matrix 85 98 99
Jones, S. T. 130 132 134
Kantorovich graph 1 6 7
Kantorovich, L. V. 2 126 131
Kedem, G. 5 15 49—51 56 88
Krawczyk method 129
Krawczyk, R. 129 132
Kronecker delta 93
Kuba, D. 55 106 130 131
Label 17 27
Label, current 45
Label, external 45
Label, internal 45
Lagrange multiplier 96
Lagrange multiplier, remainder term 36
Language, assembly 3
Language, higher-level 3
Leibniz rule 39
Leibniz, G. W. 9
Li, T. — Y. 134 135
library function 4
Library function, subroutine 4
Lie series 153
Line 27
Line, intermediate 31 60
Linear functional 23 91
Linear functional, transformation 23
Linearization 120
Lipschitz constant 118
Lipschitz constant, continuity 118
Lisp 1
List of instructions 3
List, code 4
List, procedure 39
List, subroutine call 38
Literal value 32
Magnitude 115
Mathematical programming 94
Matrix, Hessian 102
Matrix, interval 115
Matrix, Jacobian 85 98 99
Maximum norm 23 100
McCormick, G. P. 5
Mean, arithmetic 116
Mean, harmonic 116
Mechanical quadrature 138
Merging 53
Method, continuation 134
Method, Davidenko’s 134 135
Method, homotopy 134
Method, Krawczyk 129
Method, Milne's 144
Method, Newton's 97 98 100 101 102
Method, quasi — Newton 102
midpoint 116
Miller, J. C. P. 152
Milne's method 144
Milne, W. E. 144
Moore, R. E. 2 54 88 113 115 127 128 130—132 134 137—139
Multiplier, Lagrange 96
multiprocessor 8
Named variable 80
Newton 2 57 81 102 106 131 132 154
Newton operator 12 3
Newton operator, sequence 101 125
Newton's method 97 98 100 101 102
Newton's method, method, interval 129
Newton's method, three-eights rule, interval 141 149
Newton, I. 9
Nickel, K. 127 128
Node, destination 40
Node, originating 40
Node, processing 43
Nonexistence 128
Norm 23 99 100 115
Norm, constistent 104
Norm, Euclidean 23
Norm, maximum 2 3 100
Numbers, Bernoulli 145 146
Numerical integration 138
Operation, arithmetic 4
Operation, binary 5 15
Operation, unary 5
Operator 98 99
Operator, bilinear 104
Operator, Hessian 102 105
Operator, iteration 122
Operator, Newton 123
Optimal point 95
Optimal point, value 94 95
Optimization, constrained 95
Optimization, unconstrained 95
Origin 95
Originating node 40
Ortega, J. M. 126
Output code list 29 34
Owesen, J. W 84 86
P-format 116 117
Package, interval arithmetic 113
Packed code list 29
Packing 29
Packing, backward 33
Packing, forward 32
Packing, storage 44
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