Bini D., Pan V.Y. — Polynomial and matrix computations. Fundamental algorithms. Vol.1 :: Электронная библиотека попечительского совета мехмата МГУ

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Bini D., Pan V.Y. — Polynomial and matrix computations. Fundamental algorithms. Vol.1

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Название: Polynomial and matrix computations. Fundamental algorithms. Vol.1

Авторы: Bini D., Pan V.Y.

Аннотация:

Matrix and polynomial computations are fundamental to the theory and practice of computing. The authors present a systematic treatment of algorithms and complexity in these two related areas. Their study of computations with Toeplitz matrices and other dense structured matrices demonstrates the links between numerical and algebraic approaches to computation, both of which are extensively applied. Primarily a text for advanced graduate students in mathematics and computer science, but also useful for designers of algorithms and software and for researchers in algebraic computing, numerical computational mathematics, and numerical analysis.

Язык:

Рубрика: Математика/Алгебра/Вычислительная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 424

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

-SOLVE      65 142
-VECTOR      65 143
$\pm$ CONVOL      13
$\pm$ SER-MULT      21
$\tau$ matrix      186—188 215
Adjugate (adjoint) matrix      86
Adjured (expanded) Chebyshev set      16
Adjusted (expanded) Fourier set      16
ALG-FUNCTS      54
Algebraic computation tree      71
Algebraic extension      59
Algebraic functions      54
Algebraic independence approach      205
Algebraic multiplicity      87
Algebraic Newton'a iteration      49 68
Algebraic RAM      4
Algebraically closed field      83
Algorithmic error      233 234 293
ALL-INVERT      96
ALL-INVERT1      96
Amplification factor      292
Anticirculant matrix      132 215
Any precision approximation (АРА) algorithms      274—276
Approximate polynomial division      21
Approximation algorithms      5 71 251 252 257—276
Approximation by a matrix of lower rank      125
Arithmetic circuit      72
Arithmetic floating point      291—294
Arithmetic integer      241
Arithmetic modular      241
Arithmetic RAM      4
Arithmetic rational      241 242 247 289
Assignment techniques      205
Asymptotically well conditioned matrix      346
B-principle      297
b.p.d. matrix      88
Backward error analysis      253 293
Balanced factorization      99
Banded matrix      208
Barnett factorization      159
Berlekamp — Massey      48
Bezout matrix      155 156 310
Bezoutian      156
Bilinear algorithms      315
Bilinear forms      274 284 285
Bilinear steps      315
Binary integers      29 42
Binary search      150
Binary segmentation      276—279
Bit-cost/complexity      229—233
Bit-operation      232
Block matrix      92
Block matrix, triangular factorization      170
Block matrix, tridiagonalization      117 172
Boolean circuit      72 229
Boolean cost/complexity      229—233
Boolean functions      70
Boolean model      4 70 72 73 229—233
Boolean operation      72
Boolean PRAM      299
Boolean RAM      4 229—233
Brent's scheduling principle      297
C(G-H) VECTOR      261
Cauchy (generalized Hilbert) matrix      127 129
Cauchy -like matrix      180
Cauchy interpolation      45
Cauchy matrix      127 129
Caytey — Hamilton theorem      87
CH-REMNDR      27 28
CHAR-POL      96 309 318 351—353
Characteristic of a field (ring)      55
Characteristic polynomial      87 96 190 318
Chebysbev nodes      16 290
Chebysbev polynomials      53 67 66 256—260 290
Chebysbev set      16
Chebysbev-like polynomials      186 216
Chinese remainder computation      27
Chinese remainder computation, modulo powers      29
Chistov's algorithm      327
Choleski factorization      100—102 119 126
Circuit depth      73
Circuit model      72 73
Circuit size      73
Circulant matrix      132—135 215
CIRС-INVERT      134
CM-REMNDRl      29
Compact multigrid      266—273 314
Companion matrix      116
COMPL-POL-DECOMP      53
Complete decomposition of a polynomial      53
Complete orthogonal decomposition of a matrix      106 113
Composition of polynomials      32
Composition of power series      32
Compression of a generator of a matrix      111
Compressors      111
Computational cost      70 (see also time-cost)
Concurrent divide-and-conquer technique      372 381
Condition number of a matrix      91 124
Conditioning      91 233—237
Conjugate gradient      135 187
Conjugate transposed      7
Connection Machines      5
Consistent linear system      95 114
Consistent norms      90
Continued fraction      42
Convolution      13 221
Convolution via binary segmentation      277
Convolution, wrapped (positive/negative)      13
Cook's algorithm      24
Cooley — Tukey      128
Cramer's rule      238
Cristoffel — Darboux formula      136
CTH VECTOR      133
Cyclic convolution      14
Data compression      231 266 270 276
Decimation in frequency      128 221
Decimation in time      128 221
Dense structured matrix      81 82
Dense unstructured matrix      See general matrix
Depth of a circuit      73
Determinant      96 309 310 318 319 327 329 332 339 351—354 361
DFT      9 249
Diagonal matrix      86
Diagonally dominant matrix      92 212
Digits of floating point numbers      291
Discrete Fourier Transform      9
Discretization of a PDB      266
Discriminant      207
Displacement operators      175—195
Divide-and-conquer (divide-et-impera)      9 67 372 381
Divided differences      67
Down-shift matrix      127
Dual operator      179
Eigendecomposition      87
EIGENV ALUES      115
Eigenvalues      87 115
Eigenvectors      37
Elementary symmetric functions      31
Equilibration by preconditioning      288
Error analysis      233—237 291—294
Euclid's (Euclidean) algorithm      37 300 310
Euclid's (Euclidean) algorithm, matrix representation of      37
Evaluation-interpolation method      13
Exponential convergence      50
Extended Euclidean scheme      39 67 147—154 163 173 300
Extremal eigenvalues      116
EXTREME-EIGENVALUES      116
EXТ-EUCLID      40
f-circulant matrix      132—135 181
F-generator      175 218

F-rank      175 217
Factorization with no pivoting      99
Factorization with pivoting      102 107
Factorization, balanced      99
Factorization, block triangular      170
Factorization, Choleski      100—102 119 126
Factorization, complete orthogonal      106 113
Factorization, LDM      100
Factorization, LSP      103
Factorization, LU      100 212
Factorization, orthogonal      106 107
Factorization, PLU      103
Factorization, PLUP      102
Factorization, QR      107
Factorization, QRP      107
Factorization, recursive      99 100 212
Factorization, triangular      100
Fan-in      25
Fan-out      25 41
Fast Fourier Transform      9
FFT      9 221 252
FFT over finite rings      10 17 249
Field of constants      55
Floating point numbers      291—294
Floating point, arithmetic      291—294
Formal power series      18 21 32 49 157
Forward error analysis      293
Fourier matrix      12 128 220
Fourier points      9
Fourier set      69
Fourier transform      9—11
Frobenius matrix      116 155 216 220
Full rank      88
G-COMPRESS      111
Gaussian elimination      100
gcd of integers      42
gcd of several polynomials      42 151
gcd of two polynomials      36 47 147 150 155 161
GEN-DFT      14 58
General matrix      81 332
Generalized Cram — Schmidt orthogonalization      121
Generalized DFT at any number of points      14 15 59 249
Generalized Hilbert matrix      127 129 131
Generalized inverse      112
Generalized reversion of power series      50
Generalized Taylor expansion      23 31 52
Generating function of a matrix      156
Generator      108 111
Generator of length d      88
Gohberg — Semencul inversion formula      135
Gram — Schmidt orthogonalization      121
Greatest common divisor      See gcd
H-INTERP      30
H-INTERP1      45
H-REDUCE      116
h.n.d, matrix      88
Hadamard's inequality      238
Hankel matrix      48 132 155
Hankel+Toeplitz-like matrix      186 337—350
Hankel-like matrix      180 337—350
Hartley matrix      216
Hartley transform      216
Hensel — Newton's lifting      See Newton — Hensel
Hermite interpolation      30 (see also (m or
Hermite interpolation polynomial      46
Hermitian matrix      88
Hermitian nonnegative definite matrix      88
Hermitian positive definite matrix      88
Hermitian transposed      7
Hessenberg form      115 116
Hessenberg reduction      116
Hilbert-like matrix      180
Homer's rule (scbeme)      8
Homotopic techniques      349
Homotopic transformation      111
I-EIGENVALUES      117
I-POWER SUMS      34
Identity matrix      86
IDFT      11 12
Ill-conditioned matrix      236
Ill-conditioned problem      234 256 280
Induced norms      90
Inherent error      234 292
Inner product      278
Input size      4 70 72
INT DIVIDE      24
INT MULT      17
integer arithmetic      241
integer division      24
Integer multiplication      17
Integer rounding-off      252
Interpolation to a function by a polynomial      11 25 277
Interpolation via binary segmentation      277
Interpolation, generalised real      290
Interpolation, multivartate polynomial      64
Interval arithmetic      294
Inverse      112 318 346
Inverse discrete Fourier transform (IDFT)      11 128
Inverse FFT      12
Inverse tridiagonal eigenvalue problem      117
Inversion of a Toeplitz matrix      135 136
Inversion of a triangular Toeplitz matrix      134
Inversion of an f-circulant matrix      134
invert      96 318 321 346—350
Irreducible matrix      120
Iterated mod function      300
Iterated product of polynomials      12
Kernel      89
Kronecker product      185 221 265
Kronecker substitution (map)      62
KRYLOV      97
Krylov matrix      92 97
L-SQUARES      106 318
Lagrange interpolation polynomial      28 29 47
Lanczos algorithm      118
Lanczos vectors      119
Laplace rule for determinant      87
Las Vegas algorithms      5 72
Lattice      63
Laurent series      260
lcm of several polynomials      42 68 152
lcm of two polynomials      36 39 47 147 310
LDM factorization      100
Leading principal submatrix      86
Least common multiple (LCM)      See Icm
Least significant bits      271 287
Least-squares solution and orthogonal factorization      106
Least-squares solution of a linear system      106
Legendre polynomials      55
Length of a generator      85
LIN-SOLVE      95 104 128 130 318—320 342
LIN-SOLVE1      95 104 309 318
Linear recurrence      45
Linear system      95
Linear system, iterative algorithms for      262
Llifting      243 245
Loewner matrix      217
Lower triangular matrix      86
LSP factorization      103
LSP-FACTORS      103
LU factorization      100 212
LU FACTORS      100 323
M-COMPRESS      125
M-CONDITION      125
M-MULTIPLY      94
M-norm      125
M-POWERS      97
M-PRECNDTN      109
M-RANK      108 309 318 333 343 350
M-VECTOR      94

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