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| Bini D., Pan V.Y. — Polynomial and matrix computations. Fundamental algorithms. Vol.1 |
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| Предметный указатель |
 -SOLVE 65 142
-VECTOR 65 143
 CONVOL 13
SER-MULT 21
 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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