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| Hammerlin G., Hoffmann K.-H., Schumaker L.L. — Numerical Mathematics |
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| Предметный указатель |
A-posteriori bound 335
A-priori bound 335
abacus 6
Abu Jafar Mohammed Ibn Musa Al-khowarizmi 30
Acceptability of solutions 76
Ada Augusta, Countess of Lovelace 32
Admissible vector 376
Aiken code 5
Aiken, Howard Hathaway 33
Algebraic multiplicity of eigenvalues 92
Algol 33
Algorithm 1 30 33
Algorithm of Aitken — Neville 215
Algorithm of Householder 66 75
Algorithm, average behavior of an 396
Algorithm, polynomial 399
Alternant 147
Alternation theorem 147
Analog computer 6
Analog computer machines 5
Analytical engine 32
Approximation by polynomials 125 144
Approximation by rational functions 157
Approximation error 133
Approximation for functions of several variables 133
Approximation for periodic functions 133
Approximation in pre-Hilbert spaces 160
Approximation of piecewise continuous functions 167
Approximation of the first derivative 204 205
Approximation of the second derivative 205
Approximation problem in  173
Approximation theorem of Weierstrass 127
Arithmetic operation 15 19 34
Arithmetic, high precision 28
Associative operations 8
B-complementary map 12
B-splines 242 ff.
Babbage, Charles 31
Backward error analysis 26 29
Banach fixed-point theorem 332
Banach space 119
Banach, Stefan 119
Band matrix 55
Bang-bang control 375
Basis for the spline space 230
Basis point 381
Basis variable 381
Basis vectors 49
Bernoulli functions 281
Bernoulli functions, polynomials 279
Bernoulli, Jakob 282
Bernoulli, Johann 281
Bernstein operator 129 131
Bernstein operator, polynomials 127
Bernstein, S.N. 126
Bessel inequality 162
Best approximation 135 136
Best approximation, existence of a 137
Best approximation, uniqueness of a 138 ff.
Best interpolation 209
Binary arithmetic 8
Binary coding 5
Binary digit 11
binary number 11
Binary representation 2
Binary system 2 4 11
Bit 8 11
Bit chain 9
Bivariate Lagrange polynomials 225
Bolyai, W. v
Boolean algebra 8
Boolean rule 290
Boolean sum 268
Boundary knots 229
Bounded linear operator 123
Branching of a program 35
Bulirsch sequence 296
Burroughs, William Seward 7
BYTE 9 11 12
Cancellation of digits 17
carry bit 8
Central limit theorem 327
Cesaro summation 132
Characteristic polynomial 92
Chebyshev norm 119
Chebyshev polynomial of the first kind 153 154 304
Chebyshev polynomial of the second kind 171 172 312
Chebyshev system 146 174 175 176 182
Chebyshev, Pafnutii Lvovitsch 144 313
Cholesky decomposition 61
Cholesky, Andre-Louis 62
Clenshaw — Curtis formula 312
Closed orthonormal system 163
COBOL 33
Coding length 398
Column exchange 50
Column pivot search 52 53
Column sum criterion, strong 350
Column sum criterion, weak 353
Column sum norm 70
Column vector 48
Compiler 36
complete 119 163
Complete linear space 119
Complete orthonormal system 71 162 163
Complete pivoting 58
Complete system of eigenvectors 92
Complete system of orthonormal eigenvectors 80
Completeness Condition 162 163
complexity 19 36 37
Complexity measures 37
Complexity of Gauss elimination 58
Complexity of the Cholesky decomposition 63
Complexity of the QR decomposition 67
Complexity, average case 39
Complexity, worst case 39
Computation steps 40 41
Condition number 20 28 29
Condition of a matrix 73 74 87
Condition of a problem 20
Conjunction 8 9
Connection point 35
Continued fraction 23
Contraction Theorem 119 332
Contractive mapping 332
Convergence 311
Convergence condition for the SR method 361
Convergence in mean 166
Convergence of interpolating polynomials 208
Convergence of linear splines 240 256 257
Convergence of quadrature formulae 316
Convergence of the QR algorithm 110
Convergence rate of 336
Convergence speed 115
Convergence, accelerating the 338
Convergence, global 334
Convergence, linear 336
Convergence, local 333 339
Convergence, monotone 331
Convergence, quadratic 109 336
Convergence, superlinear 336
Convexity, strict 138
Cost vector 393
Cotes, Roger 286
Cramer's rule 97
Data errors 1 19 22
Data point 182
Data point polynomial 183
Data system 4 5
Data values 182
| Data vector 20
de la Vallee-poussin C. 149
de Lagrange, Josef Louis 189 281
Defect 73
Defect vector 360
Definiteness 34
Deflation 108
Derivative-free error bound 197
Diagonalizable matrix 92 105
Difference, ascending 203
Difference, backwards 202
Difference, central 203
Difference, descending 201 202
Difference, forward 200
digit 4
Digital computer 6
Direct code 5
Direct methods 47
Dirichlet kernel 132 135
Discrete approximation 152 173
Discrete approximation by trigonometric functions 178
Disjunction 8 9
Distributive operations 8
Distributivity law 29
Disvalence 8 9
Divergence, alternating 331
Divide and conquer 41
Divided difference, m-th order 189
Divided difference, of the first order 189
Documentation 35
DOUBLE PRECISION 14 15
Dynamic complexity measures 37
Eberle, M.-E. vi
Eckert, J. Presper 33
Efficiency of an algorithm 36
Eigenspace 91
Eigenvalue 71 91
Eigenvalue equation 91 92
Eigenvalue estimates 98
Eigenvalue problem 91
Eigenvalue, multiplicity, algebraic 92
Eigenvalue, multiplicity, geometric 91
Eigenvalues of a Hessenberg matrix 97
Eigenvalues of tridiagonal matrices 95
Eigenvector 71 91
Electronic analog computer 6
Electronic digital computer 6
Elimination 53
Elimination method of Gauss 47 48 54
Elimination step 52 53
Ellipsoid method 399
Equidistant interpolation points 200
Equilibration 78
Equivalence of norms 71
Erhard Schmidt norm 72
Error analyse 1 19
Error bound 73
Error damping 17 22
Error probability 327
Error propagation 345
Error zero 232
Error, absolute 13 16 22
Error, for interpolating polynomials 185 ff.
Error, for interpolating splines 256 ff.
Error, for numerical differentation 206 ff.
Error, for numerical integration 275 ff.
Error, relative 13
Estimating eigenvalues 102
Euclidean algorithm 30 31
Euclidean length 64
Euler constant 288
Euler — Maclaurin expansion 279 280
Euler, Leonhard 281
Evaluation of algorithms 33
Exchange method of Remez 150 374
Expansion in Chebyshev polynomials 154
Exponential overflow 11
Extended Chebyshev system 217 218
Extended mean-value theorem 198 201
Extrapolation 288
Extrapolation of the step size 292
Extremal property of Rayleigh quotients 108 109
Extremal property of splines 237
Extreme point 377
Fast matrix inversion 46
Fast matrix multiplication 44
Fejer operator 132f
Fejer, L. 133
Fibonacci numbers 342
Filippi formula 312
Finite continued fraction 23 24
Fixed point 332
Fixed-point arithmetic 10
Fixed-point representation 10
Floating-point arithmetic 13 23 34
Floating-point form 15
floating-point numbers 11 14 15
Floating-point numbers, double precision 12
Flow chart 34 35
FORTRAN 33
Forward error analysis 29
Fourier series expansion 169
Frobenius matrix 51
Frobenius norm 72
Fundamental theorem of approximation theory 139
Gauss algorithm 50
Gauss elimination 50 75
Gauss elimination without pivoting 60
Gauss — Jordan method 59 79
Gauss — Jordan quadrature 299
Gauss — Seidel method 353 362
Gauss — Seidel parameter 89
Gauss — Seidel relaxation 362
Gauss, Carl Friedrich 47 172
Geometric multiplicity of eigenvalues 91
Gerschgorin disks 345
Gerschgorin, S.A. 102
Gibbs phenomenon 171
Gram matrix 161
Greatest common divisor 30 31
Gregory, James 204
Gronwall's inequality 38
Gronwall's inequality, discrete form of 39
Growth of errors 22
Gunter, Edmund 6
Haar space 146 182
Haar subspace 147 148
Haar, Alfred 146
Hahn, Philip Matthaeus 7
Hermite interpolation 217
Hermite polynomials 303
Hessenberg matrix 97
Hexadecimal digit 11
Hexadecimal form 12
Hexadecimal system 4 5 11
Hilbert matrix 79
Hilbert space 120 121
Hilbert, David 122
Hirsch conjecture 395
Hoelder inequality 122
Hollerith, Hermann 32
Homogeneity 68 120
Homogeneous system of equations 49
Horner scheme 24 215 344
Householder matrix 64 93
Householder method 79 93
Householder method, with equilibration 79
Huygens, C. 288
Ignoring the singularity 309
Ill-conditioned 20
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