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Ortega J.M. — Numerical analysis: a second course
Ortega J.M. — Numerical analysis: a second course

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Название: Numerical analysis: a second course

Автор: Ortega J.M.

Аннотация:

This republication addresses some of the basic questions in numerical analysis: convergence theorems for iterative methods for both linear and nonlinear equations; discretization error, especially for ordinary differential equations; rounding error analysis; sensitivity of eigenvalues; and solutions of linear equations with respect to changes in the data.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 215

Добавлена в каталог: 21.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L_{p}$ norm      16 22
A posteriori estimates      38 50 53 59 158
Absolute norm      52
Absolute value of matrices      107
Absolute value of vectors      107
Adams — Bashforth method      82 87
Adams — Moulton method      82 87 95
Back substitution      172
Baluev, A.      163
Banach lemma      32
Bauer — Fike theorem      52
Bauer, F.      52
Boundary value problem      1 96 136
Buzbee, B.      136
Cauchy — Schwarz inequality      16
Characteristic equation      6
Cholesky decomposition      174
Class M matrix      24
Coddington, E.      70 78 195
Companion matrix      42
Complete pivoting      181 189
Condition number      29 32 35 54
Consistent method for differential equations      83ff
Consistent method, iterative      191
Consistently ordered matrix      127
Contraction      152 155 160—161
Contraction mapping theorem      153
Convergence error      3 115
Convergence factor, asymptotic      125ff
Convergence of iterative methods      115ff
Convergence of iterative methods, global      161ff
Convergence of iterative methods, local      144ff
Convergence of iterative methods, quadratic      149
Convergence of iterative methods, superlinear      149
Convex mapping      162
Convex set      142
Convex, hull      59
Courant — Fischer theorem      57
Dahlquist's theorem      95
Daniel, J.      166 195
Davidenko's method      160
Derivative (Frechet)      141
Diagonal dominance      105 120
Diagonal dominance, irreducible      105
Diagonal dominance, strict      105
Diagonal matrix      7
Dieudonne, J.      27 195
Difference equations      3 4 70 119
Differential inequality      162
discrete analogue of      96ff 111ff 136ff 150 154
Discretization error      3 79 83 88ff 96ff 111
Discretization error, global      83 92 96
Discretization error, local      83 99
Eigenvalue      6 14 42 45 101
Eigenvector      6 14 39 42 45 60 101
Eigenvector, generalized      13
Eigenvector, left and right      54
Elliptic norm      16
Equilibrated matrix      179
Equilibrated matrix, column      179
Equilibrated matrix, row      179
Error analysis, backward      182ff
Error analysis, forward      182
Euclidean norm      15
Euler's method      72 77 81
Explicit method      81
Faddeev, D.      27 195
Faddeeva, V.      27 195
Fike, C.      52
Finite difference method      1 96
Fixed point      144
Forsythe, G.      41 46 114 139 193 195
Forward reduction      170
Fox, L.      127
Franklin, J.      43
Fundamental theorem of integral calculus      142
Gantmacher, F.      27 195
Gauss — Seidel method      118 120 131 136 139 146 148
Gaussian elimination      117 169ff
Gaussian elimination, pure      169 171
Gear, C.      95 195
Generalized eigenvector      13
Gerschgorin Circle Theorem      47
Gerschgorin's theorem (for discretization error)      99 111
Givens, J.      47
Golub, G.      136
Graph      104
Graph, directed      104
Graph, strongly connected      104
Gregory, R.      35
Grid points      1 136
Growth factor      188
Hahn, W.      78 195
Henrici, P.      85 95 114 195
Hermitian matrix      7 21
Heun's method      82 92
Hilbert matrix      32 34 63
Hoelder inequality      19
Hoffman — Wielandt Theorem      58
Householder, A.      27 41 52 63 114 139 193 195
Ill conditioned      3 29 34 45
Imbedding method      159
Implicit method      81
Inner product      16
Instability      see "Stability"
Inverse      6
Irreducible matrix      103
Issacson, E.      95 114 139 195
Iterative refinement      189ff
Jacobi's method      117 120 131 135 136 139
Jordan block      12 15 67
Jordan canonical form      12 27
Kahan's theorem      122
Karney, D.      35
Keller, H.      95 114 139 195
Levinson, N.      70 78 195
Lidskii — Wielandt theorem      59
Local convergence      144ff
Localization theorem      47
Lyapunov, A.      65
M-matrix      108
Matrix norm      20
Matrix, class M      24
Matrix, companion      42
Matrix, consistently ordered      127
Matrix, diagonal      7
Matrix, equilibrated      179
Matrix, hermitian      7 21
Matrix, Hilbert      32 34 63
Matrix, irreducible      103
Matrix, nonnegative      107
Matrix, nonsingular      6
Matrix, orthogonal      7 14
Matrix, permutation      102 112
Matrix, positive definite      7 14
Matrix, reducible      102
Matrix, residual      38
Matrix, skew-symmetric      14
Matrix, Stieltjes      108
Matrix, symmetric      7 14 21 56
Matrix, triangular      7
Matrix, two-cyclic      128
Matrix, unitary      7
Maximum principle      96ff
Mean value theorem      141
Milne's method      83 87
Moler, C.      41 193 195
Monotonic norm      52
Multistep method      81
Multistep method, linear      82 85 94
Neilson, C.      136
Neumann lemma      26 107
Newton — Baluev theorem      163
Newton — Gauss — Seidel method      146 147 150
Newton — Jacobi method      2 152
Newton — Kantorovich theorem      155
Newton's method      140 144 148—151 155—158 161 163—166
Newton's method, simplified      151
Nichols, N.      127
Nonnegative matrix      107
Nonsingular matrix      6
Norm equivalence theorem      18
Norm, $L_{p}$      16 22
Norm, absolute      52
Norm, elliptic      16
Norm, Euclidean      15
Norm, matrix      20
Norm, monotonic      52
Norm, operator      52
Norm, vector      52
One-step method      81
Operator norm      20
Order      91ff
Ortega, J.      114 139 141 143 150 156 166 195
Orthogonal matrix      7 14
Osborn, J.      52
Ostrowski — Reich theorem      123
Ostrowski's theorem      145
Partial ordering      107
Partial pivoting      178ff
Perfectly conditioned      34
Permutation matrix      102 112ff
Perron's theorem      76 145
Picard's method      154
Pivoting, complete      181 189
Pivoting, partial      178ff
Point of attraction      144
Polynomial, continuity of roots      43
Positive definite matrix      7 14
Principal submatrix      63 172
Principal vector      13
Principal vector, degree of      13
Property A      128
Quadratic convergence      149
Rank      6
Rate of convergence of discretization error      91ff 100ff 112
Rate of convergence of iterative methods      125ff 140ff
Rayleigh quotient      61
Reducible matrix      102
Reduction to principal axes      10
Residual matrix      38
Rheinboldt, W.      114 139 141 143 150 156 166 195
Romanovsky's lemma      129
Rouche's theorem      42
Rounding error      3 161ff
Runge — Kutta methods      82 93
Schur's theorem      11 15
Schwartz, J.      52
Second difference quotient      2
Sherman — Morrison formula      174
Similarity transformation      7
Singular value      22
Skew-symmetric matrix      14
SOR method      121 123 127 131ff 136 139
Spectral radius      6 23
Spectrum      6
Splitting, P-regular      122
Splitting, regular      119
Splitting, weak regular      124
Stability      3 4 29 65 71
Stability of methods      86 89
Stability, asymptotic      65 71 119
Stability, numerical      4
Stability, relative      65 68 71
Stability, strong      87
Stability, weak      87
Stein's theorem      122
Steplength      81
Stieltjes matrix      108
Successive overrelaxation      see "SOR method"
Superlinear convergence      149
Symmetric matrix      7 14 21 56
TRANSPOSE      5 6
Trapezoidal rule      82
Triangular decomposition      172
Triangular matrix      7
Two-cyclic matrix      128
Unit ball      17
Unit sphere      17
Unitary matrix      7
Unstable      see "Stability"
Varga, R.      114 139 195
Vector norm      15 21
Vector, absolute value of      107
Vector, nonnegative      107
Vector, principal      13
Wasow, W.      114 139 195
Weissinger, J.      122
Wilkinson, J.      27 38 41 45 49 51 63 167 179 185 189 193 195
Young, D.      127 139 195
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