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Rall D. — Computational Solution to Nonlinear Operator Equations
Rall D. — Computational Solution to Nonlinear Operator Equations

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Название: Computational Solution to Nonlinear Operator Equations

Автор: Rall D.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1969

Количество страниц: 225

Добавлена в каталог: 29.10.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$k$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 $k$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, $k$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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