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Varga R.S. — Matrix iterative analysis
Varga R.S. — Matrix iterative analysis

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Название: Matrix iterative analysis

Автор: Varga R.S.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1962

Количество страниц: 335

Добавлена в каталог: 17.02.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$M$-matrix      85
$p$-cyclic matrix      99
$\omega$- routine      287
Accelerated Liebmann method      59
Acceleration parameters      212
Alternating-direction (ADI) methods      209
Asymptotic rate of convergence      67
Average rate of convergence      62 133 134
Backward difference method      263
Biharmonic problems      208
Block directed graph      100
Block iterative methods, Gauss — Seidel      81
Block iterative methods, Jacobi      105
Block iterative methods, Successive overrelaxation      80 194
Block tridiagonal matrix      99 102
boundary conditions      182 250
Chebyshev, polynomials      132
Chebyshev, Principle      223
Chebyshev, Semi-iterative method      138
Circulant matrix      45
Column vector      7
Commutative matrices      220
Companion matrix      48
Completely reducible matrix      43 155
Compressible flows      251
Condition number      66 95
Conjugate transposed matrix      11
Consistent approximation      267
Consistent matrix norm      10
Consistently ordered matrix      101 102
Convergence of discrete approximations      165
Convergent matrix      13
Convex, bodies      24
Convex, closure      234
Convex, polygon      234
Crank — Nicolson method      263
Critical      259
Cyclic, Chebyshev semi-iterative method      150
Cyclic, graph      51 100
Cyclic, iterative method      2 24
Cyclic, matrix      35
Cyclic, reduction      155
Deferred approach to the limit      207
Derivation of finite difference approximation, Integration      166 174
Derivation of finite difference approximation, Taylor’s series      162
Derivation of finite difference approximation, Variational formulation      167
Diagonally dominant      23
Differential corrections method      207 298
Diffusion, approximation      251
Diffusion, coefficient      251
Diffusion, equation      251
Diffusivity      251
Direct inversion, block tridiagonal matrices      196
Direct inversion, tridiagonal matrices      195
Directed graphs      19 48
Directed graphs of type      2 121
Dirichlet problem      2 202
Discrete approximation      165
Disk      9
Divergent matrix      13
Dominance ratio      287
Douglas — Rachford method      240
Douglas’ method      244
Dual mesh      207
Einzelschrittverfahren      58
Error vector      7 132
Essentially non-negative matrix      260
Essentially positive matrix      257
Estimation of parameters      283
Euclidean vector norm      8
Explicit method      263
Exponential matrix      87 254
Extrapolated Gauss — Seidel method      59
Extremal vectors      28
Factorization techniques      194
Finite multiplicative group      35
Five-point formula      186
Forward difference method      262
Forward-backward method      277
Free steering method      24
Frobenius matrix      48
Galerkin’s method      206
Gauss — Seidel method      58
Gaussian elimination      195
Generalized stochastic matrix      54
Gerschgorin Circle Theorem      16
Gesamtschrittverfahren      57
Graph theory      19
Green’s Theorem      184
Heat equation      251
Helmholtz equation      205
Hermitian matrix      11
Hexagonal mesh      193
Hilbert matrix      34
Imprimitive matrix      54
Improved three-point approximation      180
Inconsistently ordered      126 130
Indecomposable matrix      19
Index of primitivity      42
Induced iterative methods      270
Infinitesimal generator      279
Initial condition      250
Input-output matrices      280
Interfaces      174 302
Inverse power method      290
Irreducible matrix      19
Irreducibly diagonally dominant      23
Isoperimetric inequalities      291 294
Iteratively faster      62
Jacobi iterative method      57 98
Jacobi matrix      68
Jacobi normal form      13
Laplace’s equation      3 193
Length of a path      20
Leontieff matrix      280
Liebmann method      58
Linear acceleration      159
Loop      19
Major paths      121
Markov chains      25
Matrix, Differential equation      253
Matrix, norms      9 15
Maximum principle      206 280
Mesh, points      162 174
Mesh, region      183
Mesh, spacings      174
Method of lines      199 279
Method of simultaneous displacements      57
Method of successive displacements      58
Min-max, for spectral radius      32
Min-max, problem for ADI methods      223
Minor paths      121
Model problem      202
Mono tonicity principle      217
Monotone matrix      87
Natural ordering      187
nodes      19
Non-cyclic iterative method      2 24
Non-negative definite matrix      11
Non-negative matrix      26
Non-negative vector      26
Normal form, cyclic matrix      39
Normal form, reducible matrix      46
Normal matrix      15
Norms, consistent matrix norm      10
Norms, euclidean vector      8
Norms, properties of      8
Norms, subordinate matrix norm      10
Norms, unitarily invariant      15 25
Ordering vector      103
Ordinary matrix differential equation      253
Orientation of mesh lines      201
Orthogonal sot of vectors      11
Oscillation matrices      206
Ostrowski’s theorem      3 6 77
Ovals of Cassini      22
Overrelaxation      58
Pad$\acute{e}$, Rational approximations      266
Pad$\acute{e}$, Table      266
Path      19
Peaceman — Rachford Matrix      212
Peaceman — Rachford method      212 273
Perron — Froebenius theorem      30
Point, Gauss — Seidel method      58
Point, Jacobi method      57 271
Point, single-step method      58
Point, successive overrelaxation method      59 272
Point, total step method      57
Poisson’s equation      292
Positive matrix      26
Positive vector      26
Power method      287
Primitive graph      51
Primitive matrix      35
Principal square submatrix      30
Property $A^{\pi}$      97 99
Property A      97 99
Rate of convergence      67
Rayleigh quotient      290
Reducible matrix      18 45
Regular splitting      88
Relaxation factor      58 97
Relaxation method      2
Removal cross section      251
Richardson’s method      141 159
Ritz method      169 189
Rotational symmetry      192
Rounding errors      24 196
Second order Richardson method      159
Semi-discrete approximations      250
Semi-explicit      252
Semi-group theory      279
Semi-iterative method      133 159
Sparse matrix      1
Spectral norm      9
Spectral radius      9
Splitting      88
Stability      265 281
Stable matrix      265
Stein — Rosenberg theorem      70
Stieltjes matrix      85
Stochastic matrix      54
Strictly diagonally dominant      23
Strictly upper triangular matrix      46
Strongly connected directed graph      20
Subcritical      259
Subordinate matrix norm      10
Successive 2-line overrelaxation (S2LOR)      208
Successive line overrelaxation (SLOR)      199
Successive overrelaxation matrix      59 68
Successive overrelaxation method      59 105
Supercritical      259
Symmetric successive overrelaxation      275
Symmetrically non-negative matrix      43
Systematic overrelaxation      59
Three-point approximations      178
Total step method      57
Transposed matrix      11
Transposed vector      7
Tridiagonal matrix      99
Two-point boundary value problem      161 173
Unconditionally stable      265
Underrelaxation      58 92
Unisolvent functions      223
Unitarily invariant norms      25
Unitary matrix      15
Unreduced matrix      19
Unstable      281
Variational formulation      167 188
Vector convergence      8
Vector norms      8 15
Wachspress — Habetler ADI method      242
Weakly cyclic matrix      39 99 149
Young’s formula      110
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