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Delves L.M. (ed.), Walsh J. (ed.) Ч Numerical Solution of Integral Equations
Delves L.M. (ed.), Walsh J. (ed.) Ч Numerical Solution of Integral Equations

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Ќазвание: Numerical Solution of Integral Equations

јвторы: Delves L.M. (ed.), Walsh J. (ed.)

язык: en

–убрика: ћатематика/

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

ed2k: ed2k stats

√од издани€: 1974

 оличество страниц: 350

ƒобавлена в каталог: 25.06.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
A-stability      158Ч160
AbelТs 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
BesselТs inequality      48
Best approximation      57 58 116
Bi-variational method      111
Bifurcation      218 219
Block method      80 148
Boundary value problem      66 192Ч195 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      8Ч10
Characteristic value      5 8Ч10 193
Chebyshev approximation      57 60 99
Chebyshev expansion      19Ч20 22 81 250Ч251 253
ChebyshevТs method      230
Cholesky decomposition      24 25 28 38
Collocation      55 56 83 87Ч92 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 44Ч49 84 108 110
Condition number      26 37 92 125Ч126 131
Conformal mapping      267 270Ч274
Consistency      152 241
Continuation method      232Ч234
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 212Ч217 229Ч231
Convergence of sequence      44
Convergence, rate of      114Ч116 117 122 123
Convolution kernel      75 250
Critical point      232
Deferred approach to the limit      70Ч71 129 130Ч131 166 167 195
Deferred correction      69Ч70 131Ч132 144 167 195
Dense      45
Difference equations      154 158
Diffraction problem      275Ч288 321
Dirichlet problem      259 267Ч269 271 276 282
Dock problem      264Ч265
Domain      49 51
Duffing equation      220 225
Eigenvalue problem, algebraic      32Ч38 126 225 318
Eigenvalue problem, generalized      38Ч39 135 136
Eigenvalue problem, integral equation      26 108Ч114 117 123 125Ч137 177 248 282 315
Eigenvalue problem, operator      51 52
Error bounds for eigenvalues      37 38
Error bounds for integral equations      77 78 100Ч104 113Ч116 273
Error bounds for linear equations      25 26 118Ч119
Error bounds for nonlinear equations      231 235 242
Euler Ч Maclaurin formula      15 16 159
Expansion methods      80Ч95 108 122 135Ч137 180Ч181 196Ч200 238 292 325
Exterior problems      267 270 276 277 283 288 300
Faddeev equation      330Ч332
Filter factor      183 184
Finite differences      68Ч70 122 287
Finite elements      115 300Ч310
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      5Ч7 218 220 294
Fredholm equation      108 208
Fredholm equation of first kind      2Ч3 6Ч7 28 104 105 162 174 175Ч186 198 248 260Ч262
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
FubiniТs Theorem      315 317
Function space      41 42 81 108
Functional      86 109 112 113 114 182 198 226 232
Galerkin method      83Ч86 88 89 92Ч94 100 108 111 120 136 197 203 239 325
Gauss formula      286 313
Gauss Ч Rational rule      118 324
Gaussian elimination      23Ч25 27Ч28 56 59 67 248
Gaussian quadrature      14 88 117 122 201 326
Givens rotation      28
Gram matrix      84
Gram Ч Schmidt process      19 28 60
GreenТs formula      270 278 281Ч284 300 306 314
GreenТs function      193 195 219 220 224 244 301 305 322
GregoryТs formula      15 68Ч70 131 144 147 153 165Ч166
Haar condition      56
Hammerstein equation      209 219 224
Helmholtz equation      275 277Ч280 301 305 306
Hermitian operator      51 109Ч113 126
Hessenberg form, upper      36 39
Hessian operator      227
Hilbert space      46Ч49 108 116 217 293 321
Homogeneous equation      2 5 41 117 196 279 315
Householder transformation      28 29 39 60
hydrofoil, flow round      262Ч264
Hylleraas Ч 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      189Ч200 265
Integro-differential equation, partial      200Ч204
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 229Ч232
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 254Ч255 329
Knots (of splines)      55 90 137 150 159
Lagrangian interpolation      88 127 168 169
LaplaceТs equation      267 268 275 312 313
Least-squares problem      28Ч30 57 83 85 86 122 123 181 281
Legendre polynomials      19 22 88 137 203 323
Library programs      244 247Ч255
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 Ч Neumann series      4 5
Lippmann Ч Schwinger equation      323
Lipschitz condition      140 153 213 214 230 258
Logarithmic potential      268
LoveТs 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 300Ч310 312Ч319 329
Multistep method      141Ч145 147 151Ч154 190 231 252
Neumann boundary conditions      267 268 276 279 284 301 314 316
Neumann expansion      50 87
Neutron transport equation      201Ч204
Newton Ч Cotes formulae      13 74
Newton Ч Gregory formula      see УGregoryТs formula
NewtonТs method      132 215 229Ч231
Nonlinear equation      71 81Ч83 92 120Ч121 140 149 190 207Ч245 249
Norm      43 49 87 114 116 122 208 226 227
Nystrom method      80 91
One-step method      145 191 252
Operator equation      97 226Ч228 284
Orthogonal functions      5 9 18 47 48 80 112 116 177
Orthogonal functions, matrix      28 29 35
Orthogonal functions, polynomials      19 89 115
ParsevalТs Inequality      48
PeanoТs theorem      15
Picard iteration      212
Pivoting      23Ч25 28 31
PlemeljТs formula      259 260 264
PoissonТs equation      312
Polynomial approximation      12 19 22 55 59 80 87 89 102 137
Potential problem      72 76 267Ч274 279
Potential problem in three dimensions      312Ч319
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 УGaussian УGauss-Rational УGregory УMid-point УNewton УSimpson УTrapezium)
QZ algorithm      38
Radiation condition      276 278 305 322
Radiative transfer, equation of      245
RANGE      49 176
Rank of a matrix      28Ч32
Rayleigh quotient      132 135 137
Rayleigh Ч Ritz method      84 109 116 118 120 123 136 197 325
Regularization      182Ч184 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 УDeferred approach to the limit)
Runge Ч Kutta method      142 145 146 191 192 252
Scattering problem      202 275Ч277 321Ч332
Schmidt Ч Lichtenstein theory      209Ч211
SchwartzТs inequality      47 296
Secant method      232
Self-adjoint      51
Seminorm      43
Separable space      48 49
Separable space, expansion      324 331
SimpsonТs rule      13 64 67 71 72 90 128 131 143 147Ч149 155Ч159 191 272
Simultaneous iteration      34 38
Singular functions and values      10 177Ч180 184
Singular integral equation      72Ч76 132Ч134 170 249 254 255 258Ч266 327
Singular value decomposition      31 32
Singularities (in quadrature)      17 72 132
Smoothing operator      176
Splines      55 89Ч91 137 150Ч151 158Ч160
Stability      86 117Ч120 123 151Ч160
Strongly minimal system      92
Sturm sequence      35
Temple bound      114
Three-eighths rule      143 158
Trapezium rule      13 15 75 128 130Ч134 142 155Ч159 164 193 194 225 287
Triangular elements      303Ч305 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 279Ч284 314 315
Urysohn equation      82 208 210 214 218 241
Variational method      92 108 118 199 232 237 240 332
Vector space      42Ч46
Volterra equation      3 66 100 117 140 189 208 212 238 251
Volterra equation of first kind      140 162Ч174
Volterra equation of second kind      3 80 105 140Ч160 163 164 174 191 248
Waves      264 265 275 291
Waves, diffraction and scattering      275 276 277 279 282 287 288
WeierstrassТ theorem      19 22
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