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| Ortega J.M. — Numerical analysis: a second course |
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| Предметный указатель |
 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, 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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