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Kress R., Gehring F.W. — Numerical Analysis
Kress R., Gehring F.W. — Numerical Analysis

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Название: Numerical Analysis

Авторы: Kress R., Gehring F.W.

Аннотация:

This volume is intended as an introduction into numerical analysis for students in mathematics, physics, and engineering. Instead of attempting to exhaustively cover all parts of numerical analysis, the goal is to guide the reader towards the basic ideas and general principles by way of considering main and important numerical methods. Given the rapid development of numerical algorithms, a reasonable introduction to numerical analysis has to confine itself to presenting a solid foundation by restricting the presentation to the basic principles and procedures.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 1998

Количество страниц: 344

Добавлена в каталог: 05.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L_1$ norm      41
$L_2$ norm      42
A posteriori estimate      45
A priori estimate      44
Adams — Bashforth method      244
Adams — Moulton method      245
Adjoint matrix      6
Aitken’s $\Delta^2$ 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, $C[a,b]$      40
Function space, $H^1[a,b]$      275
Function space, $L^2[a,b]$      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, $l_1$      41
Norm, $l_2$      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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