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| Авторизация |
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| Rall D. — Computational Solution to Nonlinear Operator Equations |
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| Предметный указатель |
 th Derivative 110
Ablow, C.M. 86
Abstract arc 121
Abstract binomial series 114
Abstract function 94
Abstract function, linear 94
Abstract polynomial 194
Abstract polynomial equation 107
Abstract polynomial operator 108 111
Abstract power series 112
Abstract Taylor series 112
Abstract, analytic operator 194 204
Accessibility, region of 68 185
Accessible 68
Accessible, by Newton's method 185
Addition 1
Additive operator 30
Akhiezer, N.I. 57
Akilov, G.P. 210
Albasiny, E.L. 211
Albedo 75
Algebra, Banach 94 173
Algorithm, Horner's 111
Ambartsumian, V.A. 75 86
Analysis 8
Analysis, backward error 194
Analysis, forward error 194
Analytic 113
Analytic fixed-point problem 61
Analytic operator, abstract 194 204
angle 22
Angle, right 26
Anselone, P.M. 212
Approximation 10
Approximation, successive 46 47 59
Arc, abstract 121
Arithmetic fixed-point problem 60
Arithmetic, extended interval 161
Arithmetic, interval 161
assignment operator 154
Associated space 101
Backward error analysis 194
Ball, closed 16
Ball, closed unit 15
Ball, open 16
Ball, open unit 15
Banach algebra 94 173
Banach space 18 19
Banach, Stefan 18 57 58 86
Bartle, R.G. 203 212
Basis 8
Basis, Hamel 11
Basis, orthonormal 26
Bell, E.T. 86
Bellman, R.E. 211
Bilinear operator 33 102 118
Binomial series, abstract 114
Blum, E.K. 127
Bound 38 71
Boundary value condition, homogeneous 181
Boundary value problem 174
Boundary value problem, linear 174
Boundary value problem, linear elliptic 180
Boundary, condition 174
Bounded linear operator 36 38
Bounded operator 38
Bounded set 16
Bram, Joseph 211
Brown, O.E. 211
Caccioppoli, R. 58 86
Case, conservative 82
Cauchy sequence 18
Cauchy — Schwarz inequality 24
Cauchy, A.L. 58
Cebysev's method 205
Center 16
Chain rule 88
Chandrasekhar, S. 75 86
Characteristic value 201
Characteristic vector 201
Chart, flow 166
Churchill, R.V. 210
Class, equivalence 20
Code list 157
Collatz, L. 211
Column vector 33 49
Commutative 94
Compiler 157
Complete normed linear space 19
Completion 20
Component 4
Composition of operators 42 88
Computable function, interval 162
Condition, boundary 174
Condition, homogeneous boundary value 181
Condition, Lipschitz 73
Conjugate space 94
Conservative case 82
Construction 47
Continuation 78
Continuous operator 36
Contraction mapping 64 66
Contraction mapping, principle 58 65
Contraction, factor 65
Convergence map 186
Convergence, faith in 165
Convergence, numerical 165
Convergence, quadratic 190
Convergence, radius of 112
Convergence, strong 30
Convergence, weak 30
Convergent sequence 16
Convergent Series 16
Convergent, at th step 133
Convex set 21
Coordinate 4
Correction, Newton 129
Cosine 23
Courant, R. 57 211
Davis, H.T. 180 211
Davis, P.J. 86
Definition, inductive 42
Definition, natural 5
Degree of abstract polynomial equation 107
Delta, Kronecker 10
Derivative of product 88
Derivative of sum 88
Derivative, th 110
Derivative, first 87 88
Derivative, Frechet 87
Derivative, mixed second partial 115
Derivative, partial 97
Derivative, partial of order k 118
Derivative, second 109
Diagonal sequence 21
Dickson, L.E. 210
Difference operator 56
Difference, finite 62 183
Differentiable operator 88
Differential 93
Differential operator 31
Differential operator, partial 180
Differential operator, Riccati 97
Differential, Frechet 87 88
Differential, total 94
Differentiation 31
Differentiation, linearization by 129
DIMENSION 8
Direction 22 27
Dirichlet problem 181
| Discretization 10
Discriminant 24
Distance 13
distribution 31
Divergent due to inversion failure 133
Dunford, N. 56
Efficiency 48
Eigenvalue 201
Eigenvector 201
Elimination, Gaussian 54
Elliptic boundary value problem, linear 180
Entry 33
Equation, abstract polynomial 107
Equation, Laplace 181
Equation, linear 42
Equation, linear integral of Fredholm type and first kind 179
Equation, linear integral of Fredholm type and second kind 45
Equation, linear integral of Fredholm type and third kind 179
Equation, linear integral of Volterra type and second kind 52
Equation, linear, theory of 47
Equation, nonlinear integral of Hammerstein type 178
Equation, nonlinear integral of Urysohn type 179
Equation, nonlinear integral of Volterra type 172
Equation, Poisson 181
Equation, quadratic 107
Equivalence class 20
Equivalence relation 20
Equivalence, topological 16
Error 13
Error analysis, backward 194
Error analysis, forward 194
Error estimate 47 48 192
Error, percentage 13
Error, relative 13
Estimate 41
Estimate, error 47 48 192
Evaluation functional 99
Evaluation, interval 103 162
Existence 18 47 64 135
Extended interval arithmetic 161
Factor, contraction 65
Factor, improvement 139 210
Faddeeva, V.N. 57 210
Faith in convergence 165
Fenyo, I. 212
Finite differences 62 183
First kind of linear integral equation of Fredholm type 179
First, derivative 87 88
Fixed point 58
Fixed point problem, analytic 61
Fixed point problem, arithmetic 60
Flow chart 166
Fomin, S.V. 56
Formal operator 90
Forsythe, G.E. 210
Forward error analysis 194
Fourier transform 31
Fourier, series 27
Frechet, M. 88 127
Fredholm type linear integral equation of first kind 179
Fredholm type linear integral equation of second kind 45
Fredholm type linear integral equation of third kind 179
Freshet derivative 87
Freshet differential 87 88
Friedman, B. 57
Function, abstract 94
Function, generalized 31
Function, Green's 175 181
Function, interpolating 10
Function, interval 161
Function, interval, computable 162
Function, linear abstract 94
Function, scalar majorant 122
Function, spline 12
Functional 6 94
Functional, evaluation 99
Functional, linear 34
Fundamental sequence 18
Gaussian elimination 54
Gaussian integration rule 79
Generalized function 31
Geometric series 44
Glazman, I.M. 57
global 74
Goldstein, A.A. 212
Gorn, Saul 211
Gram — Schmidt orthonormalization process 28
Granville, W.A. 127
Graves, L.M. 120 127
Gray, Julia H. 155 211
Green's function 175 181
Green's integral operator 182
Green, George 175
Greenspan, D. 86 183 210
Greville, T.N.E. 57
grid 62
Grid point 62
Group, abelian 3
Group, commutative 3
Hamel basis 11
Hammerstein integral operator 95
Hammerstein type of nonlinear integral equation 178
Hardy, G.H. 57
Hellinger, E. 57
Heron of Alexandria 58 60
Hilbert space 22 26
Hilbert, David 22 57 211
Holder inequality 17
Holder, place 90
Homogeneous boundary value condition 181
Homogeneous operator 30
Horner's algorithm 111
Hyperbolic 97
Identity element 2
Identity operator 34 42
Improvement factor 139 210
IN 101
Increment 93
Indexed place holder 113
Inductive definition 42
Inequality, Cauchy — Schwarz 24
Inequality, Holder 17
Inequality, Infimum 38
Inequality, Minkowski's 14
Inequality, triangle 13
Infinite-dimensional 8
Initial value problem 169
Injection 10
Inner product 23
Inner product, space 24
Integrable 122
integral 122
Integral equation technique 172 181
Integral equation, linear, of Fredholm type and first kind 179
Integral equation, linear, of Fredholm type and second kind 45
Integral equation, linear, of Fredholm type and third kind 179
Integral equation, linear, of Volterra type and second kind 52
Integral equation, nonlinear, of Hammerstein type 178
Integral equation, nonlinear, of Urysohn type 179
Integral equation, nonlinear, of Volterra type 172
Integral operator, Green's 182
Integral operator, Hammerstein 95
Integral operator, Urysohn 97
Integral transform 32
Integral transform, linear 41
Integration rule, Gaussian 79
Integration, by parts 124
Integration, numerical 78
Interpolation 10
Interpolation, natural method of 84
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