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| Johnston R. — Numerical methods, a software approach |
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| Предметный указатель |
Accuracy 19
Adams — Bashforth formulas 248
Adams — Moulton formulas 250
Adaptive quadrature 213 221
Adaptive Romberg quadature 223
Algorithm 18
Aliasing effect 141
ANSI FORTRAN 21
Approximation 119
Approximation by exponentials 128
Approximation by piecewise polynomials 129
Approximation by polynomials 128
Approximation by trigonometric and other forms 129
B-spline 134
B-spline, package 272
Back substitution 31 37
Backward error analysis 49
banking 223
Basis 122
Basis function 122
Basis, local 131
Basis, orthogonal 127 207
beta function 199
Binary search 111
Bisection method 159
Boundary-value problem 236
Bracket 159
Brent’s method 172
Broyden’s method 189
Cancellation 12
Cautious Romberg integration 220
Characteristic polynomial 64
Cholesky factorization 58
Chopping 7
Column convergence 220
Communications vector 261
Condition number 50 84 184
Convergence 150
Cramer’s Rule 87 149
Definite integral 199
Deflation 151 174 182
Diameter 152 157
Difference equation 16 17
Differential equation 17 233
Differential equation, general solution 233
Differential equation, numerical solution 16 238
Differential equation, particular solution 234
Differential equation, series solution 235
DIMENSION 122
Divided difference 103 168 203
Divided difference, and derivative 104
Divided difference, table 102
Documentation 20
doubly linked list 60
Dynamic allocation 41
ease of use 20
Eigenvalue 26 64
Eigenvalue, dominant 74
Eigenvector 26 38 74
EISPACK package 271
Elimination 31 37
Elimination in place 34
Elliptic integral 232
EPS 8
Equivalent problem 27
error control 3
Error vector 46
Error, absolute 4 154
Error, global 240
Error, growth 48
Error, in approximation 123 135
Error, in interpolation 104
Error, inherent 3
Error, local 241
Error, propagation 29 242
Error, quadrature 203
Error, relative 4 7 46 154
Error, round-off 3 7
Error, tolerance 54
Error, truncation 3
Euler’s formula for  138
Euler’s formula for differential equations 239
EXPONENT 5
F-test 156
Fast fourier transform, (FFT) 142
Fehlberg’s method 247
Fill-in 60
Finite difference Newton method 188
fixed-point 150
Fixed-point iteration 150 169 259
Fixed-point number system 4
Floating-point number system 4
FLOP 9
Fourier coefficient 139
Fourier series 129 139
Fractional part 5
Function space 119 120 207
Gamma function 199 211
Gauss elimination and back substitution 28 31 149
Gauss elimination and back substitution, algorithm 37
Gauss quadrature 206 226
Gauss quadrature, points 208
Gauss quadrature, rules 206
Gauss — Jordan method 87
Generating set 120
Global convergence 152 180
Goodness of fit 95
Guard digit 9
Hermite polynomials 211
Hessenberg matrix 71
Hexadecimal number system 23
Hybrid method 168 172
Ill-conditioned 49 155 183 257
Improper integral 224
IMSL package 270
Initial condition 16 236
Initial-value problem 236
Instability 16
Interpolation 96
Interpolation, by cubic splines 114
Interpolation, by piecewise cubic Hermite 113
Interpolation, by piecewise linear 109
Interpolation, conditions 96
Interpolation, osculatory 106 113
Interpolation, piecewise polynomial 109 205
Interpolation, polynomial 97 201
Inverse iteration 38 74
Inverse quadratic method 171 172
Iteration 150
Iterative improvement 16 38 51
Iterative method 150
Jacobian matrix 185 257
Joints 109
K-step formula 248 252
Knots 109
Knots, variable 137
Kronecker delta 202
Laguerre polynomials 211
Laguerre’s method 179
Least-square, approximation 124
Least-square, solution 77
Length-preserving 70
linear combination 120 121
Linear dependence 122
Linear equations 26 28
Linear equations, overdetermined 26 76
Linear independence 121
LINPACK package 271
Lobatto rules 228
Local problem 241
| Local solution 242
LU decomposition 28 31
Machine epsilon 8 21
Machine hardware precision 54
Mathematical model 95
Mathematical software 1
MATLAB package 272
Matrix, band 59 132 135
Matrix, companion 194
Matrix, conjugate transpose 140
Matrix, defective 64
Matrix, determinant 32 33
Matrix, eigenvalue 64
Matrix, eigenvector 74
Matrix, Hessenberg form 71
Matrix, orthogonal 66
Matrix, permutation 31
Matrix, positive definite 58
Matrix, quasi-triangular 65
Matrix, rank 79
Matrix, similar 66
Matrix, singular value 82
Matrix, sparse 60 187
Matrix, symmetric 57
Matrix, tridiagonal 73
Matrix, unit triangular 28 36
Matrix, unitary 140
Matrix, Vandermonde 99
Matrix-vector notation 28
Mean-value theorem for derivatives 105
Mean-value theorem for integrals 203
method 18
Minimal degree algorithm 61
Minmax solution 77
MINPACK package 272
Modified Gram — Schmidt (MGS) 80 127
Muller’s method 171
Multiplier 29
Multistep formulas 248
NAG package 271
NDIM 40
Neighborhood 152 157
Newton — Cotes ruler 202
Newton — Raphson method 151 168 260
Newton’s method 185
Nonlinear equation 148
Norm,  77
Norm,  45
Norm,  45
Norm, of matrix 46
Norm, of vector 45
Norm, uniform 77
Normal equations 79
Numerical singularity 40 55
One-step, two-half steps 214 222 241 250
Operations count 22
Order of accuracy 243
Orthogonal 49
Orthogonal basis 127 207
Orthogonal functions 140 206 209
Orthogonal matrix 66
Overdetermined linear system 26 76 124
Overflow 6
Packed form 57 59
Period 138
Periodic function 138
Piecewise polynomial 109
Piecewise polynomial, cubic Hermite 113
Piecewise polynomial, cubic spline 114
Piecewise polynomial, linear 109
Piecewise polynomial, quadratic 113
Pivot element 29
Pivot vector 32
Pivotting, complete 31
Pivotting, partial 31
Pivotting, strategy 32 60
Polynomial 177
Polynomial, Hermite 211
Polynomial, Lagrange form 99 120 201
Polynomial, Laguerre 211
Polynomial, Legendre 144 211
Polynomial, nested form 97 102 177
Polynomial, Newton form 101 201
Polynomial, Tchebychev 211
Polynomial, trigonometric 138
Portability 20
Power method 74 92
Predictor-corrector pair 251
Premature termination 154
Preprocessing 62
Prime factorization 142
Propagation effect 256
Pseudo inverse 83
QR, algorithm 64 69 84
QR, factorization 67 80
QR, transformation 69
QUADPACK package 272
Quadratic equation 11 149
Quadrature 199
Quadrature, adaptive 221
Quadrature, adaptive Romberg 223
Quadrature, algorithm 212
Quadrature, composite rules 205
Quadrature, error 203 209 213
Quadrature, Gauss rules 206
Quadrature, Newton — Cotes rules 202
Quadrature, points 200
Quadrature, Romberg 214
Quadrature, rule 199
Quasi-Newton methods 188 260
Rank-one update method 191
Rate of convergence 158
Real valued function 159
RECURSIVE 223
Regula falsi method 162 165
Relative correction 54
Relative density 4
Relative separation 184
Reliability 19
Removable singularity 225
Residual 45 123 124
Residual, relative 47
Robustness 19
Romberg integration 214
Romberg table 214
Roof function 130
Root 149
Root mean square error 79 135
Rounding 7
Row convergence 217
Runge — Kutta formulas 243
Scalar function 186
Secant line 163 166
Secant method 165 168 188 260
Semilog fit 128
Separation 184
Shape preserving 70
Shooting method 266
Similarity transformation 66
Simpson’s rule 203 206
Singular value decomposition (SVD) 82
Sparse matrix algorithm 60
Spectral radius 91
Spline, basis form 131
Spline, clamped boundary 115
Spline, cubic 114 133
Spline, free boundary 115
Spline, linear 113 130
Spline, piecewise form 131
Spline-on-spline 145
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