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| Delves L.M. (ed.), Walsh J. (ed.) — Numerical Solution of Integral Equations |
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| Ïðåäìåòíûé óêàçàòåëü |
A-stability 158—160
Abel’s equation 3 162 170
Adjoint operator 51 112
Algebraic integral equation 211
Alternation property 60
Asymptotics 5 277 299
B-splines 90
Banach space 44 49 92 93 207 208 226
Bernouilli numbers 15
Bessel’s inequality 48
Best approximation 57 58 116
Bi-variational method 111
Bifurcation 218 219
Block method 80 148
Boundary value problem 66 192—195 267 276 300 308
Bounded operator 49 50
Cauchy integral formula 263 264
Cauchy principal value 6 258 259
Cauchy sequence 44 45
Characteristic function 8—10
Characteristic value 5 8—10 193
Chebyshev approximation 57 60 99
Chebyshev expansion 19—20 22 81 250—251 253
Chebyshev’s method 230
Cholesky decomposition 24 25 28 38
Collocation 55 56 83 87—92 94 125 135 137 197 239 271 286
Compact operator 51 52 93 110 293
Compatibility 178
Complete orthonormal sequence 48 53 92 110
completely continuous 51 52 92 93 284
Completeness 10 19 21 44—49 84 108 110
Condition number 26 37 92 125—126 131
Conformal mapping 267 270—274
Consistency 152 241
Continuation method 232—234
Continuous operator 50
Contraction mapping 212 214 216 231
Convergence 137 152 165 169 178
Convergence of Fourier series 21 22 115
Convergence of nonlinear iteration 210 212—217 229—231
Convergence of sequence 44
Convergence, rate of 114—116 117 122 123
Convolution kernel 75 250
Critical point 232
Deferred approach to the limit 70—71 129 130—131 166 167 195
Deferred correction 69—70 131—132 144 167 195
Dense 45
Difference equations 154 158
Diffraction problem 275—288 321
Dirichlet problem 259 267—269 271 276 282
Dock problem 264—265
Domain 49 51
Duffing equation 220 225
Eigenvalue problem, algebraic 32—38 126 225 318
Eigenvalue problem, generalized 38—39 135 136
Eigenvalue problem, integral equation 26 108—114 117 123 125—137 177 248 282 315
Eigenvalue problem, operator 51 52
Error bounds for eigenvalues 37 38
Error bounds for integral equations 77 78 100—104 113—116 273
Error bounds for linear equations 25 26 118—119
Error bounds for nonlinear equations 231 235 242
Euler — Maclaurin formula 15 16 159
Expansion methods 80—95 108 122 135—137 180—181 196—200 238 292 325
Exterior problems 267 270 276 277 283 288 300
Faddeev equation 330—332
Filter factor 183 184
Finite differences 68—70 122 287
Finite elements 115 300—310
Fixed-point problem 208 229
Fourier series 18 20 21 43 84 116 287 292
Fourier series, convergence of 21 22 115
Fourier transform 3 323
Frechet derivative 93 121 209 227
Fredholm alternative 5—7 218 220 294
Fredholm equation 108 208
Fredholm equation of first kind 2—3 6—7 28 104 105 162 174 175—186 198 248 260—262
Fredholm equation of second kind 2 4 5 7 26 41 64 65 80 98 100 102 175 193 208 248 250 263 298
Fredholm operator 49 51 52 109 116
Fredholm resolvent kernel 211 215 218
Fubini’s Theorem 315 317
Function space 41 42 81 108
Functional 86 109 112 113 114 182 198 226 232
Galerkin method 83—86 88 89 92—94 100 108 111 120 136 197 203 239 325
Gauss formula 286 313
Gauss — Rational rule 118 324
Gaussian elimination 23—25 27—28 56 59 67 248
Gaussian quadrature 14 88 117 122 201 326
Givens rotation 28
Gram matrix 84
Gram — Schmidt process 19 28 60
Green’s formula 270 278 281—284 300 306 314
Green’s function 193 195 219 220 224 244 301 305 322
Gregory’s formula 15 68—70 131 144 147 153 165—166
Haar condition 56
Hammerstein equation 209 219 224
Helmholtz equation 275 277—280 301 305 306
Hermitian operator 51 109—113 126
Hessenberg form, upper 36 39
Hessian operator 227
Hilbert space 46—49 108 116 217 293 321
Homogeneous equation 2 5 41 117 196 279 315
Householder transformation 28 29 39 60
hydrofoil, flow round 262—264
Hylleraas — Undheim theorem 110
Ill-conditioning 29 87 90 104 126 175 280 281
Ill-posed problem 163 176 177 179 181 184 262
Infinite range 249
inhomogeneous equation 108 112 120 123
Initial value problem 141
Inner product 18 19 46 49 116
Inner product space 46 93
Instability 155 157 160 179 180 181
Integral operator 26 92 93 112 207 278 315
Integro-differential equation 189—200 265
Integro-differential equation, partial 200—204
Interior problem 270 280 282 314 316
Interpolation 55 56 59 82 88 240 241
| Inverse iteration 36 38
Iterative methods 83 120 142 184 185 212 215 229—232
Iterative refinement 27 30
Jacobian matrix 227 234
Jump discontinuity 131 269 278 279 283
Kernel 2 7 49 65 67 83 108 115 117 123 129 130 140 148 177 219 286 298 300 323
Kernel, degenerate 7 94 127 128 176 324
kernel, hermitian 9 111 127
Kernel, logarithmic 72 133 134 269 273
Kernel, real symmetric 9 250
Kernel, singular 17 74 125 132 170 249 254—255 329
Knots (of splines) 55 90 137 150 159
Lagrangian interpolation 88 127 168 169
Laplace’s equation 267 268 275 312 313
Least-squares problem 28—30 57 83 85 86 122 123 181 281
Legendre polynomials 19 22 88 137 203 323
Library programs 244 247—255
Linear independence 56 80 85 94 135
Linear operator 49 50 53 97 100 120 209
Linear programming 60 83 98 101
Linear space 42 129
Liouvilie — Neumann series 4 5
Lippmann — Schwinger equation 323
Lipschitz condition 140 153 213 214 230 258
Logarithmic potential 268
Love’s equation 102 103
Majorant, scalar 210 211 213 214 228
Mid-point rule 13 157 170
Minimax solution 57 99
Minimization problem 183 232 235
Mixed boundary conditions 268 269 276
Moments, method of 85 111 112 120 123 135
Monotone operators 216 217
Multidimensional integral equation 249 285 300—310 312—319 329
Multistep method 141—145 147 151—154 190 231 252
Neumann boundary conditions 267 268 276 279 284 301 314 316
Neumann expansion 50 87
Neutron transport equation 201—204
Newton — Cotes formulae 13 74
Newton — Gregory formula see “Gregory’s formula
Newton’s method 132 215 229—231
Nonlinear equation 71 81—83 92 120—121 140 149 190 207—245 249
Norm 43 49 87 114 116 122 208 226 227
Nystrom method 80 91
One-step method 145 191 252
Operator equation 97 226—228 284
Orthogonal functions 5 9 18 47 48 80 112 116 177
Orthogonal functions, matrix 28 29 35
Orthogonal functions, polynomials 19 89 115
Parseval’s Inequality 48
Peano’s theorem 15
Picard iteration 212
Pivoting 23—25 28 31
Plemelj’s formula 259 260 264
Poisson’s equation 312
Polynomial approximation 12 19 22 55 59 80 87 89 102 137
Potential problem 72 76 267—274 279
Potential problem in three dimensions 312—319
Power method 33 34 38
Predictor-corrector method 190
Probabilistic method 185
Product integration 17 74 91 134 170 332
Projection method 92 93 239
Projection operator 53
QR algorithm 36 39
Quadrature method 121 122 125 324
Quadrature rule 12 80 100 126 127 133 141 164 286
Quadrature rule, Lobatto 14 176
Quadrature rule, Radau 14 (see also “Gaussian “Gauss-Rational “Gregory “Mid-point “Newton “Simpson “Trapezium)
QZ algorithm 38
Radiation condition 276 278 305 322
Radiative transfer, equation of 245
RANGE 49 176
Rank of a matrix 28—32
Rayleigh quotient 132 135 137
Rayleigh — Ritz method 84 109 116 118 120 123 136 197 325
Regularization 182—184 185 198 284 285
Repetition factor 158
Residual 27 37 57 81 97 99 106 122 180 183
Riemann sum 127
Robin problem 276 277 282 284
Romberg extrapolation 16 (see also “Deferred approach to the limit)
Runge — Kutta method 142 145 146 191 192 252
Scattering problem 202 275—277 321—332
Schmidt — Lichtenstein theory 209—211
Schwartz’s inequality 47 296
Secant method 232
Self-adjoint 51
Seminorm 43
Separable space 48 49
Separable space, expansion 324 331
Simpson’s rule 13 64 67 71 72 90 128 131 143 147—149 155—159 191 272
Simultaneous iteration 34 38
Singular functions and values 10 177—180 184
Singular integral equation 72—76 132—134 170 249 254 255 258—266 327
Singular value decomposition 31 32
Singularities (in quadrature) 17 72 132
Smoothing operator 176
Splines 55 89—91 137 150—151 158—160
Stability 86 117—120 123 151—160
Strongly minimal system 92
Sturm sequence 35
Temple bound 114
Three-eighths rule 143 158
Trapezium rule 13 15 75 128 130—134 142 155—159 164 193 194 225 287
Triangular elements 303—305 308
Trigonometric functions 55 80 99
Truncation error 68 127 130 142 143
Uniqueness of solution 5 6 93 176 179 207 270 275 276 279—284 314 315
Urysohn equation 82 208 210 214 218 241
Variational method 92 108 118 199 232 237 240 332
Vector space 42—46
Volterra equation 3 66 100 117 140 189 208 212 238 251
Volterra equation of first kind 140 162—174
Volterra equation of second kind 3 80 105 140—160 163 164 174 191 248
Waves 264 265 275 291
Waves, diffraction and scattering 275 276 277 279 282 287 288
Weierstrass’ theorem 19 22
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