Demmel J.W. — Applied Numerical Linear Algebra :: Электронная библиотека попечительского совета мехмата МГУ

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Demmel J.W. — Applied Numerical Linear Algebra

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Название: Applied Numerical Linear Algebra

Автор: Demmel J.W.

Аннотация:

Designed for use by first-year graduate students from a variety of engineering and scientific disciplines, this comprehensive textbook covers the solution of linear systems, least squares problems, eigenvalue problems, and the singular value decomposition. The author, who helped design the widely used LAPACK and ScaLAPACK linear algebra libraries, draws on this experience to present state-of-the-art techniques for these problems, including recommendations of which algorithms to use in a variety of practical situations.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 421

Добавлена в каталог: 26.11.2005

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Предметный указатель

Arnoldi's algorithm      119 303 305 320 360 388 389
ARPACK      385
Backward error      see “backward stability”
Backward stability      4
Backward stability bisection      230 247
Backward stability Cholesky      76 80 253 263
Backward stability convergence criterion      164
Backward stability direct versus iterative methods for Ax=b      31
Backward stability eigenvalue problem      123
Backward stability Gaussian elimination      41
Backward stability GEPP      41 46 49
Backward stability Gram — Schmidt      108 134
Backward stability instability of Cramer's rule      87
Backward stability Jacobi's method for $Ax={\lambda}x$       242
Backward stability Jacobi's method for the SVD      263
Backward stability Jordan canonical form      146
Backward stability Lanczos algorithm      306 321
Backward stability linear equations      44 49
Backward stability normal equations      118
Backward stability orthogonal transformations      124
Backward stability polynomial evaluation      16
Backward stability QR decomposition      118 119 123
Backward stability secular equation      224
Backward stability single precision iterative refinement      60
Backward stability Strassen's method      69 86
Backward stability substitution      26
Backward stability SVD      118 119 123 128
Band matrices Bauer — Fike theorem      150
Band matrices linear equations      73 76—79 81 82
Band matrices symmetric eigenproblem      185
Biconjugate gradients      321
Bidiagonal form      131 240 308 357
Bidiagonal form condition number      87
Bidiagonal form dqds algorithm      242
Bidiagonal form LR iteration      242
Bidiagonal form perturbation theory      207 242 245 246 263
Bidiagonal form qds algorithm      242
Bidiagonal form QR iteration      242
Bidiagonal form reduction      166 240 253
Bidiagonal form SVD      246 260
Bisection finding zeros of polynomials      7 30
Bisection SVD      241 242 247 249
Bisection symmetric eigenproblem      119 201 210 211 228 236 241 260
BLAS (Basic Linear Algebra Subroutines)      28 64—72 83 86
BLAS (Basic Linear Algebra Subroutines) in Cholesky      76 91
BLAS (Basic Linear Algebra Subroutines) in Hessenberg reduction      165
BLAS (Basic Linear Algebra Subroutines) in Householder transformations      137
BLAS (Basic Linear Algebra Subroutines) in nonsymmetric eigenproblem      184 185
BLAS (Basic Linear Algebra Subroutines) in QR decomposition      121
BLAS (Basic Linear Algebra Subroutines) in sparse Gaussian elimination      84
Block algorithms Cholesky      64 76 91
Block algorithms Gaussian elimination      70—72
Block algorithms Hessenberg reduction      165
Block algorithms Householder reflection      137
Block algorithms matrix multiplication      66
Block algorithms nonsymmetric eigenproblem      184 185
Block algorithms QR decomposition      121 137
Block algorithms sparse Gaussian elimination      83
Block cyclic reduction      266 328—331 333 357
Block cyclic reduction model problem      277
Boundary value problem Dirichlet      267
Boundary value problem eigenproblem      270
Boundary value problem L-shaped region      349
Boundary value problem one-dimensional heat equation      77
Boundary value problem Poisson's equation      267 325 349
Boundary value problem Toda lattice      255
Bulge chasing      169 171 213
Canonical form      139 140 145
Canonical form generalized Schur for real regular pencils      179 185
Canonical form generalized Schur for regular pencils      178 180 185
Canonical form generalized Schur for singular pencils      180 185
Canonical form Jordan      3 19 140 141 144—146 150 175 176 178 180 184 185 188 280
Canonical form Kronecker, iv      179—182 185 187
Canonical form polynomial      19
Canonical form real Schur      147 163 184 213
Canonical form Schur      3 140 146—148 152 158 160 163 175 178 180 184 185 187 188
Canonical form Weierstrass, iv      173 175 176 178 180 181 185 187
CAPSS      84
Cauchy interlace theorem      261 369
Cauchy matrices      85
Cayley transform      264
Cayley — Hamilton theorem      296
CG      see “conjugate gradients” 306
cgs      see “Gram — Schmidt orthogonalization process (classical); conjugate gradients squared”
Characteristic polynomial      140 149 296
Characteristic polynomial companion matrix      302
Characteristic polynomial of $A-{\lambda}B$       173
Characteristic polynomial of $R_{SOR(\omega)}$       290
Characteristic polynomial of a matrix polynomial      182
Characteristic polynomial secular equation      218 225 231
Chebyshev acceleration      279 294—300 331
Chebyshev acceleration model problem      277
Chebyshev polynomial      296 314 330 357 358
cholesky      2 74—76 253
Cholesky band      2 77 78 277
Cholesky block algorithm      64 91
Cholesky condition number      88
Cholesky conjugate gradients      308
Cholesky definite pencils      179
Cholesky incomplete (as preconditioner)      319
Cholesky LINPACK      62
Cholesky LR iteration      243 263
Cholesky mass spring system      179
Cholesky model problem      277
Cholesky normal equations      107
Cholesky of $T_{N}$       270 357
Cholesky on a Cray YMP      62
Cholesky sparse      80 81 277
Cholesky symmetric eigenproblem      253 263
Cholesky tridiagonal      78 331
CLAPACK      61 86 88
Companion matrix      183 302
Companion matrix block      183
Computational geometry      139 175 184 187 191
Condition number      2 4 5
Condition number convergence of iterative methods      285 312 314 317 320 351
Condition number distance to ill-posedness      17 19 23 33 86 152
Condition number equilibration      61
Condition number estimation      50
Condition number infinite      17 148
Condition number iterative refinement of linear systems      58
Condition number least squares      101 102 106 108 117 125 126 128 129 134
Condition number linear equations      32—38 46 50 87 89 105 124 132 146
Condition number nonsymmetric eigenproblem      32 148—153 189
Condition number Poisson's equation      269
Condition number polynomial evaluation      15—17 24
Condition number polynomial roots      28 29
Condition number preconditioning      317
Condition number rank-deficient least squares      101 125 126 128 129
Condition number relative, for Ax=b      6 35 54 60
Condition number symmetric eigenproblem      197
Conjugate gradients      266 278 301 306—319 351
Conjugate gradients convergence      306 312 352
Conjugate gradients model problem      277
Conjugate gradients preconditioning      317 351 354
Conjugate gradients squared      321
Conjugate gradients stabilized      321
Conjugate transpose      1
Conservation law      255 256
Consistent ordering      293
Controllable subspace      182 187
Convolution      324 326
Courant — Fischer minimax theorem      198 199 201 261
Cray      13 142 226
Cray C90/J90      13 62 82 226
Cray extended precision      27
Cray roundoff error      12 25 26 224 226
Cray square root      26 3
Cray T3 series      12 62 82
Cray YMP      62 64

DAEs      see “differential algebraic equations”
DEC symmetric multiprocessor      62 82
DEC workstations      10 12 14
Deflation      221
Deflation during QR iteration      214
Deflation in secular equation      221 237 262
Diagonal dominance      91 388
Diagonal dominance convergence of Jacobi and Gauss — Seidel      286—294
Diagonal dominance weak      289
Differential algebraic equations      175 178 185
Divide-and-conquer      13 195 211 212 217—228 231 236
Divide-and-conquer SVD      133 241 242
Domain decomposition      266 285 317 319 348—357 361
Dqds algorithm      195 243
Eigenvalue      140
Eigenvalue generalized nonsymmetric eigenproblem      173
Eigenvalue generalized nonsymmetric eigenproblem algorithms      173—184
Eigenvalue nonsymmetric eigenproblem algorithms      153—173 184
Eigenvalue nonsymmetric eigenproblem perturbation theory      148—153
Eigenvalue symmetric eigenproblem algorithms      210—237
Eigenvalue symmetric eigenproblem perturbation theory      197—210
Eigenvector      140
Eigenvector generalized nonsymmetric eigenproblem      174
Eigenvector generalized nonsymmetric eigenproblem algorithms      173—184
Eigenvector nonsymmetric eigenproblem algorithms      153—173 184
Eigenvector of Schur form      148
Eigenvector symmetric eigenproblem algorithms      210—237
Eigenvector symmetric eigenproblem algorithms perturbation theory      197—210
EISPACK      62
Equilibration      37 61
Equivalence transformation      175
Fast Fourier Transform      266 278 319 321—328 333 348 351 352 357 359—361
Fast Fourier transform model problem      277
FFT      see “fast Fourier transform”
Floating point arithmetic      2 5 9 23
Floating point arithmetic $\infty$       12 28 231
Floating point arithmetic complex numbers      11 26
Floating point arithmetic cost of comparison      50
Floating point arithmetic cost of division, square root      245
Floating point arithmetic cost versus memory operations      63
Floating point arithmetic Cray      13 26 27 226
Floating point arithmetic exception handling      12 28 231
Floating point arithmetic extended precision      14 27 45 60 224
Floating point arithmetic IEEE standard      10 241
Floating point arithmetic interval arithmetic      14 45
Floating point arithmetic Lanczos algorithm      377
Floating point arithmetic machine epsilon, machine precision, macheps      11
Floating point arithmetic NaN (Not a Number)      12
Floating point arithmetic normalized numbers      9
Floating point arithmetic overflow      11
Floating point arithmetic roundoff error      11
Floating point arithmetic subnormal numbers      11
Floating point arithmetic underflow      11
flops      5
For SVD      207—210 246—249
Gauss — Seidel      266 278 279 282—283 285—294 357
Gauss — Seidel in domain decomposition      355
Gauss — Seidel model problem      277
Gaussian elimination      31 38—44
Gaussian elimination band matrices      76—79
Gaussian elimination block algorithm      31 61—73
Gaussian elimination error bounds      31 44—58
Gaussian elimination GECP      46 49 55 56 88
Gaussian elimination GEPP      46 49 55 56 87 88 132
Gaussian elimination iterative refinement      31 58—61
Gaussian elimination pivoting      45
Gaussian elimination sparse matrices      79—83
Gaussian elimination symmetric matrices      76
Gershgorin's theorem      79 91 150
Givens rotation      119 121—123
Givens rotation error analysis      123
Givens rotation in GMRES      321
Givens rotation in Jacobi's method      233 251
Givens rotation in QR decomposition      121 135
Givens rotation in QR iteration      167 168
gmres      306 320
GMRES restarted      321
Gram — Schmidt orthogonalization process      107 377
Gram — Schmidt orthogonalization process Arnoldi's algorithm      304 320
Gram — Schmidt orthogonalization process classical      107 119 134
Gram — Schmidt orthogonalization process modified      107 119 134 231
Gram — Schmidt orthogonalization process QR decomposition      107 119
Gram — Schmidt orthogonalization process stability      108 118 134
Graph bipartite      286 291
Graph directed      288
Graph strongly connected      289
Guptri (generalized upper triangular form)      186
Hessenberg form      163 184 213 302 360
Hessenberg form double shift QR iteration      170 172
Hessenberg form implicit Q theorem      167
Hessenberg form in Arnoldi's algorithm      303 304 388 389
Hessenberg form QR iteration      165 167—173 183
Hessenberg form reduction      164—166 212 303 389
Hessenberg form single shift QR iteration      168
Hessenberg form unreduced      166
Hessenberg formin GMRES      320
Hilbert matrix      85
Householder reflection      119—123 135
Householder reflection block algorithm      133 137 165
Householder reflection error analysis      123
Householder reflection in bidiagonal reduction      166 252
Householder reflection in double shift QR iteration      170
Householder reflection in Hessenberg reduction      212
Householder reflection in QR decomposition      119 134 135 157
Householder reflection in QR decomposition with pivoting      132
Householder reflection in tridiagonal reduction      213
HP workstations      10
IBM 370      9
IBM RS6000      5 14 27 68 95 133 184 236
IBM SP-2      62 82
IBM workstations      10
Ill-posedness      17 23 33 34 86 148
Implicit Q theorem      167
Impulse response      178
Incomplete Cholesky      319
Incomplete LU decomposition      319
Inertia      202 208 228 247
Intel 8086/8087      14
Intel paragon      62 73 82
Intel Pentium      14 60
Invariant subspace      145 147 153 154 156—158 189 207
Inverse iteration      155 162
Inverse iteration SVD      242
Inverse iteration symmetric eigenproblem      119 211 215 228—232 236 237 241 260 363
Inverse power method      see “inverse iteration”
Irreducibility      286 288—290
Iterative methods for $Ax={\lambda}x$       363—389
Iterative methods for Ax=b      265—361
Iterative methods for Ax=b convergence rate      281
Iterative methods for Ax=b splitting      279
Jacobi's method (for $Ax={\lambda}x$ )      195 210 212 232—237 260 263
Jacobi's method (for Ax=b)      6 278 279 281—282 285—294 357
Jacobi's method (for Ax=b) in domain decomposition      355
Jacobi's method (for Ax=b) model problem      277
Jacobi's method (for the SVD)      242 249—254 263
Jordan canonical form      3 19 140 141 144—146 150 175 176 178 180 184 185 188 280
Jordan canonical form instability      146 178
Jordan canonical form solving differential equations      176
Korteweg — de Vries equation      260
Kronecker canonical form      179—181 185 187
Kronecker canonical form solving differential equations      181
Kronecker Canonical Form, iv      182
Kronecker product      274 358
Krylov subspace      266 278 300—321 351 354 360 363—389
Lanczos algorithm      119 304—306 308 310 320 360 364—389
Lanczos algorithm nonsymmetric      321 388
LAPACK      6 61 62 86 87 153
LAPACK dlamch      13
LAPACK sbdsdc      242
LAPACK sbdsqr      242 243

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