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| Àâòîðèçàöèÿ |
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| Ïîèñê ïî óêàçàòåëÿì |
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| Goldberg M.A. (ed.) — Solution Methods for Integral Equations |
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| Ïðåäìåòíûé óêàçàòåëü |
Abel’s equation 30 37 172 239
Abel’s inversion formula 37
Adams — Moulton method 207 209
Adjoint boundary value problem 316
Adjoint differential equation 313
Adjoint operator 14 87 157
Adjoint problem 311—312
Aerodynamic forces 138
Aerodynamic work 136
Aerodynamics 34 109 147
Aeroelastic force 123
Airfoil equation 34 113
Airfoil polynomials 117
Airfoil(s) 110—111 147—148
Algebraic equations, linear 7 11 15—16 94—95 99 102 175 207 212
Algebraic equations, nonlinear 42—45 280
Algebraic Riccati equation 293 295
Ambarzumian integral equation 209—210
Automatic error control 28
b and h functions 213—215
Banach lemma 25
Banach space 8 19 92 323 326
Banach — Steinhaus theorem 21
Basis functions 11—12 14 22 31 118 140 144 187 229 239
Best approximation 237
Biased estimates 185
Bifurcation point 210
Bland’s collocation method 110 149
Bland’s integral equation 123 126
Block-by-block methods 226
Boundary integral method 205
Boundary-value method 17—18 303
Boundary-value problem 84 87—88 110—114 196 315 317 322 324
Bounded operator 118 324 326
Canonical function 88 96
Carleman — Vekua regularization 90 98 100
Cauchy integral formula 200
Cauchy principal value 83—84 86—87 90 94 96 120 128
Cauchy problem 196 199 200 204 218 322 330 341
Cauchy — Schwarz inequality 22 121 137
Chebyshev polynomials 22 33 101 236—237
classification of integral equations 2—10 287—301
Collectively compact operators 25—26
Collocation 7—8 11—12 14 20—21 23—24 26 31—33 42 110 114—117 126 129 131 134 149 151
Compact operator 9 20—21 24 36 92 110 120 123
Complete orthonormal basis 22 118 229 239
Conditioning 31 133—134
Consistency conditions 89 91 99—100
Contracting operator 69
Contraction mapping theorem 136
Convergence, acceleration 27—30 149—157
Convergence, criterion 77
Convergence, of Neumann series 70—72
Convergence, theory 19—27 103 126 149 232
Convolution equations 245 321—338
Convolution kernel 236 335
Cramer’s Rule 269 321
Decomposable kernel 227
Deflection functions 137
Degenerate kernel 6—7 12—14 18 24 29 99 197 247 250 266 270 299 305
Density function 171 176 178
Determinant 269 326
Differential equation 18 48 197 200 205 207 215 225 245 273 306 331
Differential-difference equation 178 196
Dirichlet problem 205—207 218
Displacement kernel 61—80 210—212
Distribution function 173
Dominant equation 89 97
Dominant part 84 87
Downwash 112 130 137—138 149
Dual space 11
Eigenfunction 38 198 200—201 203 272 278
Eigenvalue 3 38 64—67 91 191 198 201 261 272 274 277 319 337 342—343
Equation of the first kind, Fredholm 36—40 183—193
Equation of the first kind, Volterra 30 37 49—50 172 238—239
Equation of the second kind, Fredholm 3—33 59—81 84 88 91—92 99 110 118 198 203 206 208 212 217 257 285 287 303
Equation of the second kind, Volterra 46—49 197 226 228—232 246 258 276 283 308
Error bounds 19 25—26 29 33 45 95 125 149 153—154 188 231 251
Extrapolation 28 148 150 159—160
Fourier approximation 230
Fourier coefficients 229
Fourier cosine transform 65
Fourier transform 67 112
Frechet derivative 43
Fredholm alternative 123 125 267 273—274 276—278 281 309 315
Fredholm determinant 260 265 268
Fredholm integral equation, of the first kind 36—40 183—193
Fredholm integral equation, of the second kind 3—33 59—81 84 88 91—92 99 110 118 198 203 206 208 212 217 257 285 287 303
Fredholm integral equation, quasi- 88
Fredholm numerator 266
Fredholm resolvent 18 29—30 150 157 198—199 203—204 208 211 257—285 299 319—320
Fredholm theory 110 198 315 318
Fujita’s equation 184 189—190
Fundamental function 88 96—97
Galerkin’s method 8 12 14 19 22—24 31 33 101—103 110 124—129 132 149 153 228
Gauss — Markov estimate 183—184
Gaussian quadrature 16 201 207 209
GCV estimate 187—188
Generalized inverse 184 317
Goodness criteria 186
Goursat problem 240
Green’s function 63 73 273 276—278 305 320
Hadamard’s inequality 261
Hammerstein equation 40—48 228 279
Hilbert kernel 94
Hilbert space 68 116—118 124 128 184 326
Hilbert — Schmidt operator 63 119—120 155
Hilbert — Schmidt theory 61
III-conditioning 36 94 151 183—184 186—187
III-posed problem 36—40 110 183—193 317
Imbedding, equations 195—223 197
Imbedding, interval length 17—18 329
Imbedding, invariant 196 326 340
Imbedding, method 198
Imbedding, parameter 17—18 197—198
Initial-value method 17—18 226—228 225—243 245—255 303
Initial-value problem 197—205 207—209 215 220 227 239 245—255 237-238 333
Inner product 14 68 115 128
Integral equation, Abel’s 30 37 172 239
Integral equation, Ambarzumian 209
Integral equation, Fredholm 3 36 84 110 183 195 257 287 303
Integral equation, Fujita’s 184 189—190
Integral equation, Hammerstein 40 228 279
Integral equation, linear 3—33 36 49 59 83 109 147 169 183 195 225 245 257 287 303
Integral equation, nonlinear 40 195 225 245 303
Integral equation, singular 33 83 109 147
Integral equation, Urysohn 40
Integral equation, Volterra 30 37 49 225 245
Integrodifferential equation 39 204—205 208 217—218 236 322 342
Interpolation 11 15—16 19 21 42—43 236—237
Invariant theory 290
| Inverse problems 217
Jacobi polynomials 103 115
Jacobi — Gauss quadrature 116 131 135
Kernel approximation 5—8 19 23 230 240
Kernel evaluation 48—49 235 245
Kernel, convolution 236—238 335
Kernel, decomposable 227 235
Kernel, degenerate 6—7 12—14 18 24 29 99197 247 250 266 270 299 305
Kernel, displacement 61—80 210—212
Kernel, fundamental 289
Kernel, Hilbert 94
Kernel, iterated 257
Kernel, Possio 151
Kernel, semidegenerate 7 197 303
Kernel, simple separable 262 265 280 283 semidegenerate”)
kernel, symmetric 198 262—273
kernel, weakly singular 22 91
Kussner — Schwarz solution 138—142
Kutta condition 34 114
Lagrange interpolation 11 16
Landahl’s method 152
Laser 198—202
Least squares 8 13 39—40 131 187 318
Lebedev — Ufliand problem 207
Lift 123 136 138 140 158
Linearization 344—345
LQC problem 289 292—293
Matrix, circulant 188
Matrix, hat 186 188—189
Matrix, Vandermonde 130
Method of moments 8 229
Mildly ill-posed problem 37
Milne — Thompson equation 218—219
Minimization problem 185 187
Minimum variance unbiased estimate 183
Monte Carlo method 189
Multiple scattering 195 215—216 218
Multiple Volterra integral equation 240—241
Neumann series 61—81 259—260
Newton’s method 42—45 136 200
Noether’s theorem 87—88
Norm, Holder 95 100
Norm, matrix 31—32
Norm, operator 70
Norm, sup 11
Norm, vector 31—32
Normal distribution 186
Normal equations 39
Null space 88—89 91 96 309 311
Numerical differentiation 185
Nystrom interpolation 16 42—43
Nystrom method 18 42—46
Operator, adjoint 14 87 157
Operator, bounded 118 324 326
Operator, collectively compact 25—26
Operator, compact 9 20—21 24 36 92 110 120 123
Operator, contracting 69
Operator, finite rank 24 187 276 326
Operator, Hilbert — Schmidt 68 119—120 150
Operator, projection 9—10 12—13 125 153 240 317
Orthogonal functions 20 101 117—118 120 127 144 229
Packing fraction 176
Parking fraction 176
Parseval’s formula 90 98
Parseval’s theorem 122
Particle size statistics 169
Perron — Frobenius theorem 70
Pitching moment 136 138
Poincare — Bertrand formula 90 98
Possio equation 150
Possio kernel 151
Press 187—188
Principal components method 185
Product integration 15—16 43
Projection method 8 14 20 27 29 41—42 45 124—134 158
Projection operator 9—10 12—13 125 153 240 317
Quadrature, method 7 24—26 28 42
Quadrature, rule 15—16 94 116 131 133 135 207 209 218 332
Quasi-Fredholm equation 88
Radiative transfer 19 84 196
Rational approximation 94—95
Rayleigh — Ritz method 64—68 198
Regression, method 183 185—189
Regression, ridge 186—189
Regular part 84 87
Regularization, Carleman — Vekua 90 98 100
Regularization, Kantorovich 29
Regularization, Landahl 150 152—154
Regularization, Tikhonov 39—40 185 188—189
Residual 10 13 124 127 152
Resolvent, Fredholm 18 29—30 150 157 199 203—204 208 211 257—285 299 319—320
Resolvent, Volterra 261 263 265 268 276 281
Reverse flow theorem 150
Riccati equation 197 218 287 291 295 299 326 329 332 337
Riccati group 288 290 292—293
Riccati transformation 322 324 331 334 338
Ridge estimate 185
Riemann boundary-value problem 87—88
Runge — Kutta method 47—49 201 206 236 245—246 251
Saltikov’s method 175
Self-adjoint problem 279 236—237 239
Seminorm 39 185
Sherman — Morrison — Woodbury formula 284
Shooting method 280
Singular integral equation 33—36 83—169
Singularity subtraction 15 43 151—152
Smoothing 183—194
Sobolev  function 211
Sohngen inversion formula 114 137—138 152 154
Sokhotski — Plemelj formulas 86 88 96
Splines 12 93 143 189 226 236
Splitting method 60
Stability 33
Step function 148
Step size 206 235
Step-by-step method 50—51 226
Stereology 169
Sturm — Liouville problem 274
Subset selection 185 187—188
Successive approximations 212 232
Synthetic method 59—81
Taylor series 19 237 250 252
Tensor product 326
Trace 260
Two-point boundary-value problem 18 20 298 303—343
Urysohn equation 40
Vandermonde matrix 130
Variable step integrator 251
Variational problem 40 196
Volterra integral equation of the first kind 30 37 49—50 172 238—239
Volterra integral equation of the second kind 46—49 197 226 228—232 258 276 283 308
Zand Y functions 210—211 235—239
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