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Goldberg M.A. (ed.) Ч Solution Methods for Integral Equations
Goldberg M.A. (ed.) Ч Solution Methods for Integral Equations

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Ќазвание: Solution Methods for Integral Equations

јвтор: Goldberg M.A. (ed.)

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1979

 оличество страниц: 360

ƒобавлена в каталог: 25.06.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
AbelТs equation      30 37 172 239
AbelТs inversion formula      37
Adams Ч Moulton method      207 209
Adjoint boundary value problem      316
Adjoint differential equation      313
Adjoint operator      14 87 157
Adjoint problem      311Ч312
Aerodynamic forces      138
Aerodynamic work      136
Aerodynamics      34 109 147
Aeroelastic force      123
Airfoil equation      34 113
Airfoil polynomials      117
Airfoil(s)      110Ч111 147Ч148
Algebraic equations, linear      7 11 15Ч16 94Ч95 99 102 175 207 212
Algebraic equations, nonlinear      42Ч45 280
Algebraic Riccati equation      293 295
Ambarzumian integral equation      209Ч210
Automatic error control      28
b and h functions      213Ч215
Banach lemma      25
Banach space      8 19 92 323 326
Banach Ч Steinhaus theorem      21
Basis functions      11Ч12 14 22 31 118 140 144 187 229 239
Best approximation      237
Biased estimates      185
Bifurcation point      210
BlandТs collocation method      110 149
BlandТs integral equation      123 126
Block-by-block methods      226
Boundary integral method      205
Boundary-value method      17Ч18 303
Boundary-value problem      84 87Ч88 110Ч114 196 315 317 322 324
Bounded operator      118 324 326
Canonical function      88 96
Carleman Ч Vekua regularization      90 98 100
Cauchy integral formula      200
Cauchy principal value      83Ч84 86Ч87 90 94 96 120 128
Cauchy problem      196 199 200 204 218 322 330 341
Cauchy Ч Schwarz inequality      22 121 137
Chebyshev polynomials      22 33 101 236Ч237
classification of integral equations      2Ч10 287Ч301
Collectively compact operators      25Ч26
Collocation      7Ч8 11Ч12 14 20Ч21 23Ч24 26 31Ч33 42 110 114Ч117 126 129 131 134 149 151
Compact operator      9 20Ч21 24 36 92 110 120 123
Complete orthonormal basis      22 118 229 239
Conditioning      31 133Ч134
Consistency conditions      89 91 99Ч100
Contracting operator      69
Contraction mapping theorem      136
Convergence, acceleration      27Ч30 149Ч157
Convergence, criterion      77
Convergence, of Neumann series      70Ч72
Convergence, theory      19Ч27 103 126 149 232
Convolution equations      245 321Ч338
Convolution kernel      236 335
CramerТs Rule      269 321
Decomposable kernel      227
Deflection functions      137
Degenerate kernel      6Ч7 12Ч14 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      205Ч207 218
Displacement kernel      61Ч80 210Ч212
Distribution function      173
Dominant equation      89 97
Dominant part      84 87
Downwash      112 130 137Ч138 149
Dual space      11
Eigenfunction      38 198 200Ч201 203 272 278
Eigenvalue      3 38 64Ч67 91 191 198 201 261 272 274 277 319 337 342Ч343
Equation of the first kind, Fredholm      36Ч40 183Ч193
Equation of the first kind, Volterra      30 37 49Ч50 172 238Ч239
Equation of the second kind, Fredholm      3Ч33 59Ч81 84 88 91Ч92 99 110 118 198 203 206 208 212 217 257 285 287 303
Equation of the second kind, Volterra      46Ч49 197 226 228Ч232 246 258 276 283 308
Error bounds      19 25Ч26 29 33 45 95 125 149 153Ч154 188 231 251
Extrapolation      28 148 150 159Ч160
Fourier approximation      230
Fourier coefficients      229
Fourier cosine transform      65
Fourier transform      67 112
Frechet derivative      43
Fredholm alternative      123 125 267 273Ч274 276Ч278 281 309 315
Fredholm determinant      260 265 268
Fredholm integral equation, of the first kind      36Ч40 183Ч193
Fredholm integral equation, of the second kind      3Ч33 59Ч81 84 88 91Ч92 99 110 118 198 203 206 208 212 217 257 285 287 303
Fredholm integral equation, quasi-      88
Fredholm numerator      266
Fredholm resolvent      18 29Ч30 150 157 198Ч199 203Ч204 208 211 257Ч285 299 319Ч320
Fredholm theory      110 198 315 318
FujitaТs equation      184 189Ч190
Fundamental function      88 96Ч97
GalerkinТs method      8 12 14 19 22Ч24 31 33 101Ч103 110 124Ч129 132 149 153 228
Gauss Ч Markov estimate      183Ч184
Gaussian quadrature      16 201 207 209
GCV estimate      187Ч188
Generalized inverse      184 317
Goodness criteria      186
Goursat problem      240
GreenТs function      63 73 273 276Ч278 305 320
HadamardТs inequality      261
Hammerstein equation      40Ч48 228 279
Hilbert kernel      94
Hilbert space      68 116Ч118 124 128 184 326
Hilbert Ч Schmidt operator      63 119Ч120 155
Hilbert Ч Schmidt theory      61
III-conditioning      36 94 151 183Ч184 186Ч187
III-posed problem      36Ч40 110 183Ч193 317
Imbedding, equations      195Ч223 197
Imbedding, interval length      17Ч18 329
Imbedding, invariant      196 326 340
Imbedding, method      198
Imbedding, parameter      17Ч18 197Ч198
Initial-value method      17Ч18 226Ч228 225Ч243 245Ч255 303
Initial-value problem      197Ч205 207Ч209 215 220 227 239 245Ч255 237-238 333
Inner product      14 68 115 128
Integral equation, AbelТs      30 37 172 239
Integral equation, Ambarzumian      209
Integral equation, Fredholm      3 36 84 110 183 195 257 287 303
Integral equation, FujitaТs      184 189Ч190
Integral equation, Hammerstein      40 228 279
Integral equation, linear      3Ч33 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 204Ч205 208 217Ч218 236 322 342
Interpolation      11 15Ч16 19 21 42Ч43 236Ч237
Invariant theory      290
Inverse problems      217
Jacobi polynomials      103 115
Jacobi Ч Gauss quadrature      116 131 135
Kernel approximation      5Ч8 19 23 230 240
Kernel evaluation      48Ч49 235 245
Kernel, convolution      236Ч238 335
Kernel, decomposable      227 235
Kernel, degenerate      6Ч7 12Ч14 18 24 29 99197 247 250 266 270 299 305
Kernel, displacement      61Ч80 210Ч212
Kernel, fundamental      289
Kernel, Hilbert      94
Kernel, iterated      257
Kernel, Possio      151
Kernel, semidegenerate      7 197 303
Kernel, simple separable      262 265 280 283 semidegenerateФ)
kernel, symmetric      198 262Ч273
kernel, weakly singular      22 91
Kussner Ч Schwarz solution      138Ч142
Kutta condition      34 114
Lagrange interpolation      11 16
LandahlТs method      152
Laser      198Ч202
Least squares      8 13 39Ч40 131 187 318
Lebedev Ч Ufliand problem      207
Lift      123 136 138 140 158
Linearization      344Ч345
LQC problem      289 292Ч293
Matrix, circulant      188
Matrix, hat      186 188Ч189
Matrix, Vandermonde      130
Method of moments      8 229
Mildly ill-posed problem      37
Milne Ч Thompson equation      218Ч219
Minimization problem      185 187
Minimum variance unbiased estimate      183
Monte Carlo method      189
Multiple scattering      195 215Ч216 218
Multiple Volterra integral equation      240Ч241
Neumann series      61Ч81 259Ч260
NewtonТs method      42Ч45 136 200
NoetherТs theorem      87Ч88
Norm, Holder      95 100
Norm, matrix      31Ч32
Norm, operator      70
Norm, sup      11
Norm, vector      31Ч32
Normal distribution      186
Normal equations      39
Null space      88Ч89 91 96 309 311
Numerical differentiation      185
Nystrom interpolation      16 42Ч43
Nystrom method      18 42Ч46
Operator, adjoint      14 87 157
Operator, bounded      118 324 326
Operator, collectively compact      25Ч26
Operator, compact      9 20Ч21 24 36 92 110 120 123
Operator, contracting      69
Operator, finite rank      24 187 276 326
Operator, Hilbert Ч Schmidt      68 119Ч120 150
Operator, projection      9Ч10 12Ч13 125 153 240 317
Orthogonal functions      20 101 117Ч118 120 127 144 229
Packing fraction      176
Parking fraction      176
ParsevalТs formula      90 98
ParsevalТs theorem      122
Particle size statistics      169
Perron Ч Frobenius theorem      70
Pitching moment      136 138
Poincare Ч Bertrand formula      90 98
Possio equation      150
Possio kernel      151
Press      187Ч188
Principal components method      185
Product integration      15Ч16 43
Projection method      8 14 20 27 29 41Ч42 45 124Ч134 158
Projection operator      9Ч10 12Ч13 125 153 240 317
Quadrature, method      7 24Ч26 28 42
Quadrature, rule      15Ч16 94 116 131 133 135 207 209 218 332
Quasi-Fredholm equation      88
Radiative transfer      19 84 196
Rational approximation      94Ч95
Rayleigh Ч Ritz method      64Ч68 198
Regression, method      183 185Ч189
Regression, ridge      186Ч189
Regular part      84 87
Regularization, Carleman Ч Vekua      90 98 100
Regularization, Kantorovich      29
Regularization, Landahl      150 152Ч154
Regularization, Tikhonov      39Ч40 185 188Ч189
Residual      10 13 124 127 152
Resolvent, Fredholm      18 29Ч30 150 157 199 203Ч204 208 211 257Ч285 299 319Ч320
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 292Ч293
Riccati transformation      322 324 331 334 338
Ridge estimate      185
Riemann boundary-value problem      87Ч88
Runge Ч Kutta method      47Ч49 201 206 236 245Ч246 251
SaltikovТs method      175
Self-adjoint problem      279 236Ч237 239
Seminorm      39 185
Sherman Ч Morrison Ч Woodbury formula      284
Shooting method      280
Singular integral equation      33Ч36 83Ч169
Singularity subtraction      15 43 151Ч152
Smoothing      183Ч194
Sobolev $\Phi$ function      211
Sohngen inversion formula      114 137Ч138 152 154
Sokhotski Ч 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      50Ч51 226
Stereology      169
Sturm Ч Liouville problem      274
Subset selection      185 187Ч188
Successive approximations      212 232
Synthetic method      59Ч81
Taylor series      19 237 250 252
Tensor product      326
Trace      260
Two-point boundary-value problem      18 20 298 303Ч343
Urysohn equation      40
Vandermonde matrix      130
Variable step integrator      251
Variational problem      40 196
Volterra integral equation of the first kind      30 37 49Ч50 172 238Ч239
Volterra integral equation of the second kind      46Ч49 197 226 228Ч232 258 276 283 308
Zand Y functions      210Ч211 235Ч239
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