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| Авторизация |
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| Поиск по указателям |
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| Rall D. — Computational Solution to Nonlinear Operator Equations |
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| Предметный указатель |
Interval arithmetic 161
Interval arithmetic, extended 161
Interval computable function 162
Interval evaluation 162
Interval function 161
Inverse 43
Inversion operator 96
Inversion, of linear operators 50
Inversion, of power series 204
Iteration 130
Iteration operator, modified Newton 199
Iteration operator, Newton 185
Iteration, method of 57 59
Jacobian matrix 93
k-Linear operator 101
Kalaba, R.E. 211
KantoroviS, L.V. 57 128 135 199 210 212
Katzenjammer 201
Kernel 32 94
kernel, resolvent 46
Kind, first, of linear integral equation of Fredholm type 179
Kind, second, of linear integral equation of Fredholm type 45
Kind, second, of linear integral equation of Volterra type 52
Kind, third, of linear integral equation of Fredholm type 179
Knopp, Konrad 127 212
Kolmogorov, A.N. 56
Kronecker delta 10
Lagrange interpolating polynomial 11
Lancaster, P. 197 212
Laplace equation 181
Laplace operator 31
Lebesgue 21 27 214
Lebesgue integral 21 27 214
Lebesque measure 215
Legendre polynomial 30
Length 12
Lighthill, M.J. 57
LIMIT 16
Line segment 21 121
Linear boundary value problem 174
linear combination 8
Linear dependence 8
Linear elliptic boundary value problem 180
Linear equation 42
Linear equation, theory of 47
Linear functional 34
Linear independence 8
Linear integral equation, of Fredholm type, and first kind 179
Linear integral equation, of Fredholm type, and second kind 45
Linear integral equation, of Fredholm type, and third kind 179
Linear integral equation, of Volterra type and second kind 52
Linear integral transform 41
Linear operator 30 102
Linear operator, bounded 36 38
Linear operator, inversion of 50
Linear space 1 3
Linear space, complex 3
Linear space, normed 12
Linear space, real 3
Linear, abstract function 94
Linearization 128
Linearization, by differentiation 129
Lipschitz condition 73
List, code 157
Littlewood, J.E. 57
local 74
Lohr, Lydia R. 210
Longley, W.R. 127
Lovitt, W.V 57
MacDuffee, C.C. 127
Magnitude 13
Majorant function, scalar 122
Majorant series, scalar 112 195
Map, convergence 186
Mapping, contraction 64 66
Matrix 31
Matrix, Jacobian 93
Maximum principle 181
McCalla, T.R. 211
Mean 102 104
Mean value theorem 120
Measure, Lebesgue 215
Measure, zero 122
Mesh size 183
Method modified form of Newton's 198
Method of interpolation, natural 84
Method of iteration 57 59
Method of successive substitutions 58 59
Method, Cebysev's 205
Method, Newton's 130
Method, tangent 129
Method, variant 198
Metric 12
Milne, W.E. 86
Minkowski's inequality 14
Mixed second partial derivative 115
Modified form of Newton's method 198
Modified Newton iteration operator 199
Modified Newton sequence 199
Moler, C.B. 210
Moore, R.E. 155 162 211 213
Moore, R.H. 211
Morris, Max 211
Mosaic 89
Multilinear operator 102
Multiple solution 190
n-Dimensional 8
Natural method of interpolation 84
Necepurenko, M.I. 212
Negative 2
Nemyckii operator 95
Net 62
Neumann series 44
Newton correction 129
Newton iteration operator 185
Newton iteration operator, modified 199
Newton sequence 130
Newton sequence, modified 199
Newton's method 130
Newton's method, modified 198
Newton's method, variant of 198
Nilpotent 53
Noble, B. 86 174 210 211
Node 78
Noncommutative 94
Nonlinear integral equation, of Hammerstein type 178
Nonlinear integral equation, of Urysohn type 179
Nonlinear integral equation, of Volterra type 172
Nonlinear operator 34
Nonsingular 34 102
Norm 12 38
Norm, Euclidean 14
Norm, max 17
Norm, Minkowski 14
Normal vector 26
Normed linear space 12
Normed linear space, complete 19
Null space 34
Numerical convergence 165
Numerical integration rule 78
Onto 34
Operator 6
Operator, abstract analytic 194 204
Operator, abstract polynomial 108 111
Operator, additive 30
Operator, assignment 154
Operator, bilinear 33 102 118
Operator, bounded 38
Operator, bounded linear 36 38
Operator, continuous 36
| Operator, difference 56
Operator, differentiable 88
Operator, differential 31
Operator, fixed point of 58
Operator, formal 90
Operator, Green's integral 182
Operator, Hammerstein integral 95
Operator, homogeneous 30
Operator, identity 34 42
Operator, inversion 96
Operator, k- linear 101
Operator, Laplace 31
Operator, linear 30 102
Operator, modified Newton iteration 199
Operator, multilinear 102
Operator, Nemyckii 95
Operator, Newton iteration 185
Operator, nonlinear 34
Operator, partial differential 180
Operator, projection 61
Operator, quadratic 106
Operator, Riccati differential 97
Operator, shift 56
Operator, trilinear 102
Operator, Urysohn integral 97
Operator, zero 34
Order of numerical integration rule 7 8
Origin 2
Orthogonal 26
Orthogonal, projection 27
Orthonormal basis 26
Orthonormal set 26
Orthonormalization, Gram — Schmidt process for 28
Ostrowski, A.M. 128 210
Partial derivative 97
Partial derivative, mixed second 115
Partial derivative, of order k 118
Partial differential operator 180
Partition 10
Parts, integration by 124
Permutation 102 104
Perpendicular 26
Perry, C.L. 86
Petryshyn, W.V. 57
Picard sequence 73
Picard, E. 58
Place holder 90
Place holder, indexed 113
Pohozaev, S.I. 86 181 183 211
Point 1
Point, fixed 58
Point, grid 62
Poisson equation 181
Polynomial equation, abstract 107
Polynomial operator, abstract 108 111
Polynomial, abstract 194
Polynomial, Lagrange interpolating 11
Polynomial, Legendre 30
Power series, abstract 112
Power series, inversion of 204
Power series, reversion of 204
Principle, contraction mapping 58 65
Principle, maximum 181
Problem, boundary value 174
Problem, Dirichlet 181
Problem, initial value 169
Problem, linear boundary value 174
Problem, linear elliptic boundary value 180
PRODUCT 94
Product space 5
Product, cartesian 5
Product, derivative of 88
Product, inner 23
Product, of operators 42 88
Product, scalar 23
Projection 9
Projection operator 61
Projection, into  (or  ) 61
Projection, orthogonal 27
Quadratic convergence 190
Quadratic equation 107
Quadratic operator 106
Quasilinearization 129
Quotient, Rayleigh 203
Rabinowitz, P. 86
RADIUS 16
Radius, of convergence 112
Rail, L.B. 57 86 127 210 211 212
RANGE 34
Rayleigh quotient 203
Reciprocal 42
Region of accessibility 68 185
Reiter, A. 155 163 211
Relation, equivalence 20
Representative 20
Resolvent kernel 46
Reversion of power series 204
Riccati differential operator 97
Riemann 15 122
Riemann integral 15 122
Riesz, F. 40 56
Right angle 26
Rosser, J.B. 127
Row vector 33 49
Row-by-column rule 32 35
Rule, chain 88
Rule, Gaussian integration 79
Rule, numerical integration 78
Rule, row-by-column 32 35
Rule, Simpson's 85
Rule, three step 91
Saaty, T.L. 211
Safiev, R.A. 212
Samansku, V.E. 212
scalar 3
Scalar field 3
Scalar majorant function 122
Scalar majorant series 112 195
Scalar multiplication 1
Scalar product 23
Schroder, J. 212
Schwartz, J.T. 56
Second derivative 109
Second kind, of Fredholm type linear integral equation 45
Second kind, of Volterra type linear integral equation 52
Second partial derivative, mixed 115
Segment, line 21 121
Sequence, Cauchy 18
Sequence, convergent 16
Sequence, diagonal 21
Sequence, fundamental 18
Sequence, modified Newton 199
Sequence, Newton 130
Sequence, Picard 73
Series, abstract binomial 114
Series, abstract power 112
Series, abstract Taylor 112
Series, convergent 16
Series, Fourier 27
Series, geometric 44
Series, Neumann 44
Series, scalar majorant 112 195
Set, bounded 16
Set, convex 21
Set, orthonormal 26
Shift operator 56
Simple solution 188
Simpson's rule 85
singular 35
Size, mesh 183
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