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| Kress R., Gehring F.W. — Numerical Analysis |
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| Предметный указатель |
 norm 41
 norm 42
A posteriori estimate 45
A priori estimate 44
Adams — Bashforth method 244
Adams — Moulton method 245
Adjoint matrix 6
Aitken’s  method 117
Algebraic multiplicity 36
Aubin — Nitsche Lemma 282
B-spline 173
Backward substitution 12 15
Bairstow method 113
Banach space 40
Banach — Steinhaus theorem 314
Banach’s fixed point theorem 43
Bernoulli polynomial 207
Bernstein polynomial 180
Best approximation 47
Bezier curve 181
Bezier points 181
Bezier polygon 181
Bezier Spline 183
Bijective operator 46
Boundary value problem 258
Boundary value problem, weak solution 277
Bounded operator 33
Bounded set 29
Cauchy sequence 40
Cauchy — Schwarz inequality 30
Cea’s lemma 273
Characteristic polynomial 36 249
Chebyshev polynomial 204 223
Chebyshev quadrature 223
Cholesky elimination 19
Classical Jacobi method 131
Closed ball 29
Closed set 28
Closure 28
Collectively compact operators 294
Collocation method 302
Collocation points 302
Compact operator 288
Complete pivoting 15
Complete set 40
Computer-aided geometric design 179
Condition number 80
Conjugate gradient method 285
Consistency 235 245 246
Consistency, order 235 245 246
Consistently ordered matrix 64
Continuous operator 32
Contraction number 43
Contraction operator 43
Convergence order 108 238
Convergent quadrature 198
Convergent sequence 27
Convex hull 181
Convex set 98
Cyclic Jacobi method 132
de Casteljau algorithm 183
Defect correction iteration 69
Defect correction principle 69
Dense set 28
Diagonal matrix 16
Diagonalizable matrix 133
Diagonally dominant 56
Diagonally dominant, strictly 56
Diagonally dominant, weakly 59
Difference equation 248
Difference equation, stable 248
Direct methods 5 119
Discrepancy principle 85
Distance 27
Divergent sequence 27
Divided differences 154
Eigenvalue 36
Eigenvector 36
Elimination methods 5
Equicontinuous 289
Equivalent linear system 12
Equivalent norm 27
Euclidean norm 26
Euler method 231
Euler method, implicit 233
Euler method, improved 234
Euler — Maclaurin expansion 209
Explicit method 233
Extrapolation method 212 216
Fast Fourier Transform 167
Fibonacci numbers 256
Finite difference method 262
Finite element method 279
Fixed point 43
Forward differences 182
Forward elimination 13 14
Fourier series 52
Fourier transform, discrete 167
Fourier transform, fast 167
Fredholm integral equation 287
Fredholm integral equation, first kind 287 312
Fredholm integral equation, second kind 287
Friedrich inequality 282
Frobenius norm 127
Frozen Newton method 109
Fully discrete method 274
Function space, ![$C[a,b]$](/math_tex/fbeb56df8cf1724a777f83396b15495982.gif) 40
Function space, ![$H^1[a,b]$](/math_tex/6e6a51d3138b423f6c11d6096d629ef482.gif) 275
Function space, ![$L^2[a,b]$](/math_tex/6cb70440b67cc96434676d10a57ac8f582.gif) 42
Galerkin method 272
Gauss — Chebyshev quadrature 205
Gauss — Jordan elimination 18
Gauss — Legendre quadrature 205
Gauss — Lobatto quadrature 223
Gauss — Radau quadrature 223
Gauss — Seidel method 57
Gauss — Seidel method with relaxation 62
Gaussian elimination 11 14
Gaussian quadrature 201
Gaussian quadrature, composite 207
Geometric multiplicity 36
Global convergence 95
Global error 238
Global error, maximal 238
Gram — Schmidt orthogonalization 31
Hermite interpolation operator 161
Hermite interpolation polynomial 160
Hermite — Birkhoff interpolation polynomial 186
Hermitian matrix 37
Hessenberg matrix 144
Hessian matrix 114
Heun method 234
Hilbert matrix 79
Hilbert space 40
Horner scheme 110
Householder matrix 20
Ill — conditioned linear system 81
Ill — posed problem 77
Implicit method 233
Initial value problem 228
Injective operator 46
Inner product 29
Interpolation operator 157 302
Interpolation operator, trigonometric 169
Interpolation polynomial, Hermite 160
Interpolation polynomial, Hermite — Birkhoff 186
Interpolation polynomial, Lagrange 153
Interpolation polynomial, Newton 155
Interpolation polynomial, trigonometric 163
Interpolatory quadrature 190
| Inverse interpolation 186
Irreducible matrix 59
Iterative methods 5 119
Jacobi method 55
Jacobi method with relaxation 61
Jacobi method, classical 131
Jacobi method, cyclic 132
Jacobi method, damped 71
Jacobian matrix 99
Kernel 287
Kernel, degenerate 315
kernel, weakly singular 291
Lagrange factor 153
Lagrange interpolation polynomial 153
Least squares method 10
Left triangular matrix 18
Legendre polynomial 205
Levenberg — Marquardt method 114
LIMIT 27
Linear convergence 108
Linear interpolation 158
Linear operator 32
Linear system, equivalent 12
Linear system, triangular 12
Lipschitz condition 228
Lipschitz constant 228
Lipschitz continuous 43
Local convergence 95
Local discretization error 235
Lotka — Volterra equations 255
Lower triangular matrix 18
LR decomposition 18
Mandelbrot set 118
Matrix norm 34
Matrix, adjoint 6
Matrix, consistently ordered 64
Matrix, diagonal 16
Matrix, diagonalizable 133
Matrix, hermitian 37
Matrix, Hessenberg 144
Matrix, Hessian 114
Matrix, Hilbert 79
Matrix, Householder 20
Matrix, irreducible 59
Matrix, Jacobian 99
Matrix, left triangular 18
Matrix, lower triangular 18
Matrix, normal 127
Matrix, permutation 19
Matrix, positive definite 19 37
Matrix, positive semidefinite 37
Matrix, reducible 59
Matrix, right triangular 18
Matrix, symmetric 19
Matrix, transposed 6
Matrix, tridiagonal 7
Matrix, unitary 20
Matrix, upper triangular 18
Matrix, Vandermonde 186
Maximum norm 26 41
Mean value theorem 99
Midpoint rule 206
Milne Thomson method 245
Modified Newton method 109
Moore — Penrose inverse 84
Muitigrid methods 74
Multiplicity, algebraic 36
Multiplicity, geometric 36
Multistep method 243
Multistep method, stable 251
Neumann series 46 51
Neville scheme 156
Newton interpolation polynomial 155
Newton method 102
Newton method, frozen 109
Newton method, modified 109
Newton — Cotes quadrature 191 222
Norm 26
Norm,  41
Norm,  42
Norm, equivalent 27
Norm, Euclidean 26
Norm, Frobenius 127
Norm, maximum 26 41
Norm, stronger 50
Norm, vector 26
Normal equations 49
Normal matrix 127
Normed space 26
Nystroem method 245 296
Open ball 29
Open set 28
Operator 32
Operator norm 33
Operator, bijective 46
Operator, bounded 33
Operator, compact 288
Operator, continuous 32
Operator, contraction 43
Operator, injective 46
Operator, linear 32
Operator, strictly coercive 269
Operator, surjective 46
Ordinary differential equation 226
Orthogonal 31
Orthogonal projection 48
Orthogonal system 31
Orthonormal system 31
Parseval equality 52
Partial pivoting 15
Peano kernel 221
Permutation matrix 19
Pivot element 14
Pivoting, complete 15
Pivoting, partial 15
Polygon method 231
Polynomial, Bernoulli 207
Polynomial, Bernstein 180
Polynomial, Chebyshev 204 223
Polynomial, Legendre 205
Positive definite matrix 19 37
Positive semidefinite matrix 37
Power method 133
Pre-Hilbert space 29
Predictor corrector method 234
Projection method 272 303
Pseudo-inverse 84
QR algorithm 133
QR algorithm, deflation 144
QR algorithm, shift 144
QR decomposition 19
Quadratic convergence 108
Quadrature points 190
Quadrature weights 190
Quadrature, Chebyshev 223
Quadrature, convergent 198
Quadrature, Gauss — Chebyshev 205
Quadrature, Gauss — Legendre 205
Quadrature, Gauss — Lobatto 223
Quadrature, Gauss — Radau 223
Quadrature, Gaussian 201
Quadrature, interpolatory 190
Quadrature, Newton — Cotes 191 222
Quadrature, Romberg 213
RANGE 32
Rank one methods 110
Rayleigh — Ritz method 285
Rectangular rule 210
Reducible matrix 59
Regularization parameter 86
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