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| Collatz L. — Functional analysis and numerical mathematics |
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| Предметный указатель |
 net 81
Abelian group 27
Absolute error 100
Accumulation point 19
Achieser, N.I. 72 76 414 456 464
Adjoint operator 109
Agmon, S. 456
Aitken, A.C. 368 457
Akilow, G.R. 459 464
Albrecht, J. 228 244 248 363 367 368 379 457
Alternating behavior 354
Alternating direction 248
Alternative theorem 91
Antitone 350
Antosiewicz, H.A. 206 457
Approximation 12 44 410ff
Approximation, linear 413
Approximation, rational 415
Approximation, theorem of Weierstrass 72
Associative law 27
Assortment problem 9
Asymptotic behavior 7
Attractive fixed-point 201 345
Aumann, G. 457
Averaging operator 114 195
Banach algebra 32
Banach space 56 58
Banach, St. 457
Basis 66
Bauer, F.L. 164 457
Beckert, H. 361 457
Behnke, H. 25 79 457
Berg, L. 457
Bergman, St. 75 457
Bessel’s equation 67
Bessel’s inequality 44
Bifurcation of tubes 6
Birkhoff, G. 51 228 248 457
Bittner, L. 457
Bohl, E. 371 374 375 457
Boundary condition 6
Boundary condition, homogeneous 6 123
Boundary point 235
Boundary value problem, linear 6
Boundary value problem, nonlinear 6 251 288 340 404
Boundary value problem, semihomogeneous 251
Bounded operator 87
Bounded variation 60
Bram, J. 454 464
Brouwer, L.E.J. 357 457
Brouwer’s fixed-point theorem 357 454
Bukovics, E. 457
Capacity 8
Cartwright, M.L. 457
Cauchy convergent 54
Cauchy formula 130
Cauchy problem 261
Cauchy sequence 54
Center 438
Central difference operator 115
Chain rule 271
Characteristic equation 139 171
Characteristic initial value problem 262
Characteristic number 171
Chebyshev approximation 14 410 433 442 444
Chebyshev approximation, rational 416
Chebyshev polynomial 418
Chebyshev quadrature formula 109
Chordal distance 25 79
Closed hull 18
Closed operator 110
Closed set 18
Coddington, E.A. 118 457
Coefficients, determination of 11
Collatz, L. 5 136 139 143 157 164 183 206 234 240 257 317 336 344 444 458
Column-sum criterion 230
Combinatorics 10
Commutation relation 97
Commutator 186
Commuting operators 89
Compact 76 450
Compact, relatively 76
Complete (orthonormal system) 65
Complete (set) 55
Complete ordering 45
Completely continuous integral operator 127
Completely continuous operator 124 371
Completeness relation 67
Concave (function) 50
Concave (operator) 335
Condition number 100 185
Conformal mapping 12
Connected grid region 235
Conormal 122
Consistent matrix norm 169
Continuity of a functional 77
Continuity of an operator 87
Continuity of distance 61
Contraction 213
Convergence 52
Convergence in a pseudometric space 53
Convergence, strong 76
Convergence, uniform 55
Convergence, weak 75
Convex body 165
Convex hull 452
Convex operator 335
Convex set 28
Cooke, R.G. 97 241 458
Couple (force) 29
Coupling mechanism 11
Courant, R. 129 159 458
Courant’s maximum-minimum principle 154
Cyclically ending iteration 221
Darboux’s differential equation 196
Davis, Ph. 109 129 131 458
Day, M.M. 199 358 458
De La Vallee Poussin 463
Decomposable matrix 229 376
Defect 12 225 334
Definiteness of eigenvalue problems 159
Definiteness of norms 30
Dense 19
Derivative, Frechet 268
Derwidue, L. 361 458
Deviation from normality 185
Dieudonne, J. 176 269 464
Difference method 233
Difference operator 114
Difference operator, central 115
Differential equation 5
Differential equation, elliptic 57 233 383
Differential equation, hyperbolic 260 398
Differential equation, parabolic 393
Differential operator 117
Dijkstra, E.W. 10 458
DIMENSION 28
Dirichlet principle 136
Discrete points 307
Discrete T-approximation 433 442
Displacement operator 114
Distance, (continuity of) 61
Distance, chordal 25
Distance, Distance, from a set 63
Distance, Euclidean 32
Distributive law 27
Divergence 120
Divergence theorem (Gauss) 122
Divided differences (operator) 207 307
Divisor 47 50
| Domain of attraction 201 284
Domain of definition 86
Double pyramid 430
Dual vector norm 179
Dueck, W. 102 458
Dunford, N. 452 458
Ehrmann, H. 100 297 298 458
Eigen element (vector) 91 142
Eigenvalue problem 7 137 273 325
Eigenvalue problem and rational T approximation 431
Eigenvalue problem, definite 159
Eigenvalue problem, general 137
Eigenvalue problem, selfadjoint 139
Eigenvalue problem, special 139 140
Elliptic differential equation 57
Elliptic differential equation, nonlinear 383
Elliptic geometry 60
Equations 2
Equations with denumerably many unknowns 5 241
Equations, nonlinear 224
Equicontinuity 80
Euclidean distance 32
Euclidean vector norm 167
Euler’s expression 277
Evaluation of expressions 14
Exchange method 439
Expansion by least squares 71
Expansion by least squares, in terms of an orthonormal system 66ff
Expansions 11
Extended Bessel equation 68
Extrapolation 363
Extremum problems 8 134
Extremum property of eigenvalues 150
Fichera, G. 458
Fixed point theorem 200
Fixed point theorem, Brouwer 361 454
Fixed point theorem, Schauder 357 454
Fixed point, attractive 201
Fixed point, repulsive 201
Fomin, S.V. 196 460
Force couple 29
Forces in a plane 28
Forsythe, G.E. 234 246 458
Fourier analysis 11
Fourier coefficients 69
Frank, P. 12 458
Frechet derivative 267
Frobenius, G. 458
Function, admissible 157
Function, almost periodic 75
Functional 77
Functional determinant 275
Galerkin’s equations 161
Gauss — Seidel iteration 225
Gauss’ formulas 109
General eigenvalue problem 137
Generalized orthogonality 138
Geometry, elliptic 60
Geometry, hyperbolic 27
Gericke, H. 51 458
Gerisch, W. 196 459
Glasmann, I.M. 76 456
Gloistehn, H. 459
Golomb, M. 459
Golub, G.H. 248 459
Gradient 275
Graph 10
Green’s formula 122
Green’s function 6 95 129 351 404
grid 234
Group iteration 239
Guderley, K.G. 7 459
Haar’s function system 73
Haemmerlin, G. 131 133 459
Hahn — Banach theorem 277
Hale, I.K. 459
Halmos, P.R. 464
Hamiltonian 96
Hamming, R.W. 413 459
Hankel transform 117
Haussdorff space 20
Heat equation 397
Heinrich, H. 459
Hellwig, G. 459
Henrici, P. 459
Hermitean 171
Hermitean method 344 368 379 444
Hidden periods 13
Higher derivatives 269
Hilbert space 56ff
Hilbert, D. 129 159 458
Hille, E. 459
Hoelder inequality 16 17 181
Holomorphic function 57 129 292
Homogeneity 30
Homogeneity of a boundary condition 123
Homogeneity of an operator 86
Householder, A.S. 164 457 459
Huaux, A. 361 459
Hull, closed 18 452
Hull, convex 452
Hyperbolic differential equation 260 398
Hyperbolic geometry 61
Hyperbolic metric 27
Identity operator 3
Improved difference method 368
Inclusion for the minimum deviation 418
Inclusion theorem for eigenvalues 143
Inclusion theorem for Newton’s method 338
Inequalities, systems of 420
Inequality, Bessel 44
Inequality, Hoelder 16
Inequality, Minkowski 16 32
Inequality, Schwarz 34
Infimum 46
Infinite linear systems of equations 5 241
Initial value-boundary value problems 263
Integrable function 40
Integral equation 5 258
Integral equation, nonlinear 259 373
Integral operator 94
Integral operator, completely continuous 127
Integral transform 275
Integrodifferential equation 6
Integrodifferential operator 95
Interior normal 6
Interior point 19
Interpolation 12 129
Interpolation, polynomial 12 306
interval 46
Inverse element 27
Inverse operator 91
Inverse transformation 91
Isometry 112
Isotone 350
Iterated vector 182
Iteration, simple 224
Iteration, single-step cyclic 224
Iterative methods 101 200ff
Iterative methods, order of 290
Jackson, D. 45 71 459
Jacobi iteration 225
Jacobian 275
Kaczmarz, St. 459
Kalaba, R. 334 459
Kantorovitch, L.W. 242 317 459 460 464
Kincaid, W.M. 306 460
Kirchberger, P. 416 425 460
Knobloch, H.W. 460
Knoedel, W. 9 460
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