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| Daniels R.W. — Introduction to numerical methods and optimization techniques |
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| Предметный указатель |
Absolute error 11
Active constraint 266—269
Adams method 132 156 163
Adams method, program 160
Adams — Bashford 172
Adams — Moulton method 172
Adaptive quadrature 139
Augmented matrix 23
Automatic error control 159
Back substitution 21 25 see
Backward difference function 97
Bairstow's method 57—64
Bairstow's method, program 61
BASIC 4
batch mode 5
Bisection method 43 see
Boole's rule 137
Boundary-value problem 169—171
Box, M.J. 202 274
Brigham, E.O. 91
Calahan, D.A. 281
Carnahan, B. 98
Central difference equation 109 147
Centroid 184
Charalambous, C. 285
chebyshev 138 256—262
Chua, L.O. 36
Coefficient matching 201
Condition number 37
Conjugate directions 232
Constrained optimization 265—281
Conte, S.D. 37 57 99 159
Contraction 186
Corrector equation 131—134
Cramer's rule 16—17
Crout reduction 29—36
Crout reduction, program 34
Cube test function 195
Cubic spline see "Spline functions"
Daniels, R.W. 181
Dantzig 183
Determinant 22
Difference equation 149
Difference function 74
Difference operator 74
Difference table 77—78
Differential equations 143—174
Differentiation 103—112
Direct method 37
DOUBLE PRECISION 7
Elementary row operations 22 23 39
Elliptic integral 126
Equiripple 261
Error analysis 6—11 49 98 105 119 122 137 see
Error function 179
Euler method 144—146 see
expansion 186
Explicit methods 172
Exterior-point algorithm 279
Extrapolation 71
Faddeeva, V.N. 37
Feasible region 266
Fiacco, A.V. 285
Filon's method 138
Fleischer, P.E. 183
Fletcher — Powell 226—232
Fletcher — Powell, program 229
Forsythe, G.E. 139 254
FORTRAN 4
Forward difference function 42
Forward elimination 21 25 see
Fourier interpolation program 95
Fourier series 91—97 99
Fowler, M.E. 173
Fox, R.L. 285
Gamma function 125
Gauss elimination 19—29
Gauss elimination, program 27
Gauss — Jordan 21
Gaussian probability density function 125
Gaussian quadrature 134—137
Gaussian quadrature, program 136
Gear, C.W. 173
Gerald, C.F. 285
Global error 118
Global minimum 221
Golden section method 65—67
Golden section method, program 66
Gottfried, B.S. 228
Gradient 208—211
Gradient-projection method 267
Grove, W.E. 286
Gunston, M.A.R. 36
Hamming, R.W. 64 67 98 99 107 173
Hermite polynomial 138
hessian 227
Hildebrand, F.B. 98
Householder, A. 98
Identity matrix 17
Ill-conditioned 37 254
Implicit methods 172
Inactive constraints 266—269
Integration 115—139
| interactive mode 5
Interior-point algorithm 279
Interpolating polynomial 71
Interpolating polynomial, method of 104—106
Interpolation 71—99
Interval halving 2 see
Inverse 19 29
Inverse interpolation 85—86
iterative 2 37 44—45
Jacobian 240
Jensen, R.W. 281
Kowalik, J. 286
Lagrange interpolation program 84
Lagrange polynomials 82—85
Laguerre polynomials 138
Least-p th 181 237—262 see
Least-p th, program 246
Least-squares 86—89 99 238—241 252—256 see
Legendre polynomials 138
Liou, M.L. 90 99
Local error 118
Local minimum 179 221
Lorenge diagram 98
Lower triangular matrix 30
LU decomposition 30 see
Maclaurin series 257
Matrix 17—19
McCormick, J.M. 138
Modified Euler method 151—153
Muller's method 50—57
Muller's Method, program 55
N th-order differential equation program 167
Nelder, J.A. 183
Newton — Gregory interpolation program 80
Newton — Gregory polynomial 78—82 104
Newton's method 45—50
Newton's method, program 48 64
Newton—Raphson 45
Normal probability density function 125
Normalized variable 73—74
Objective function 179
Orthogonal 93
Panel 116
Peckham, G. 262
Penalty function 276—280
Pennington, R.H. 90
Pierre, D.A. 286
Pivot 24
Polak, E. 286
Powell test function 196
Predictor equation 131—134
Quadratic interpolation 50—57 206—208
Quadratic interpolation, program 52
Quadrature 134
Rainville, E.D. 172
Ralston, A. 286
Reflection 184
Relative error 11
Romberg prediction 127—129
Rosenbrock test function 195
Roundoff errors 6
Runge — Kutta method 153—156
Runge — Kutta method, program 155
Scalar product 211
Scaling 88 223
Scheid, F. 286
Secant method 65
Sensitivity analysis 7 12
Shift operator 75
Shooting method 173
shrink 187
Significant figure 7
Simplex method 183—190 205
Simplex method, program 188
Simpson's rules 121—125 129
Simpson's rules, program 123
Singular value decomposition 254
Sparse matrix 33—36 281
Spline Function 89—91 98
Square-root method 37
Stability analysis 147—151
Steepest-descent method 211—220
Steepest-descent method, program 215
Stewart, G.W. 36
Stiff differential equations 173
Stroud, A.H. 138
SUMT 277
Symmetric matrix 18
Taylor series 8 81 172
Test functions 195—202
Tew arson, R.P. 30
Transformations 269—276
Transient 2
TRANSPOSE 17
Trapezoidal method see "Modified Euler method"
Trapezoidal rule 10 116—120 129 138
Trapezoidal rule, program 119
Truncation error 6
Undetermined coefficients 107—111 129—131 134
Unimodal 65
Upper triangular matrix 30
Vector 18
Weight 181 237
Whittle, P. 286
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