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| Hammerlin G., Hoffmann K.-H., Schumaker L.L. — Numerical Mathematics |
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| Предметный указатель |
Improper integrals 302
Indirect methods 47
Inequality of wirtinger 264
Inner product 120
Input 30 34 40 41
integer variables 10
Integral representation for the interpolation polynomial 220
Integrals with weight functions 307
Integration over a tetrahedron 325
Integration over a triangle 325
Integration over an infinite interval 307
Integration over standard domains 324
Interior knot 229
Interpolating polynomials, Aitken — Neville 215
Interpolating polynomials, error bound for 185 ff.
Interpolating polynomials, Gregory — Newton I 202
Interpolating polynomials, Gregory — Newton II 203
Interpolating polynomials, Lagrange 288
Interpolating polynomials, Newton 189
Interpolation 182
Interpolation by polynomials 183
Interpolation by rational functions 24
Interpolation conditions 182 184
Interpolation in the complex plane 220
Interpolation on rectangular grids 224
Interpolation problem 175 182
Interpolation remainder formula of Kowalewski 194
Interpolation theorem of Schoenberg — Whitney 254
Interpolation, bilinear 227
Interpolation, existence, uniqueness 224
Interpolatory quadrature 273
Interval arithmetic 27 29
Interval solution of linear systems 347
Jacobi method 99 104 349 350 361
Jacobi method, classical 99 101
Jacobi method, cyclic 102
Jacobi polynomial 302
Jacobi rotation 98 99
Jacobi, Carl Gustav 99
Jacobian matrix 334
Karmarkar algorithm 399
Kepler's barrel rule 282
Kepler's equation 330
Kepler, Johannes 7 282
Knot sets 229
Korovkin, P.P. 126 129
Lagrange function 89
Lagrange multiplier 109
Lagrange polynomial 188
Laguerre polynomial 303
Landau symbols 37 38
Landau, E. 126
Least squares approximation by linear splines 258
Least squares fitting by polynomials 175
Least squares fitting method 173
Least squares splines of higher degree 263
Lebesgue, H. 126
Legendre polynomial 163 164 297 298
Leibniz rule 191
Leibniz rule for derivatives 199
Leibniz, Gottfried Wilhelm 7
Linear approximation 139
Linear correlation 176
Linear functional 123
Linear monotone operator 129
Linear operator 123
Linear optimization 57
Linear regression 176
Linear system of equations 48
Linear system of equations, over-determined 83
Linear system of equations, under-determined 83
Linearity 120
Lipschitz bounded 334
Local bases 243
Logic 8
Lord Napier of Merchiston 6
Lower Hessenberg matrix 55
Lower triangular form 55
LR algorithm 110 114
LR decomposition 64
Mac Laurin, Colin 282
Machine interval 28
Machine number 12 28
Machine program 36
Mantissa 10 12 14 15
Matrix, decomposable 351
Matrix, indecomposable 351
Matrix, irreducibly diagonally dominant 56
Matrix, multiplication 37 41 51
Matrix, nonnegative 355
Matrix, norm, natural 70 348
Matrix, with property A 366
Mauchly, John W. 33
Max-min search 37
Mean square error 161
Mean-value theorem 334
Memory 10 12 32
Memory, complexity 37
Method error 1 20
Method of Krylov 110
Method of least squares 172 173
Metric 118
Minimal deviation 137
Minimal property of orthonormal polynomials 166
Minimal property of the Chebyshev polynomials 154
Minimal property of the Legendre polynomials 165
Minimization problem 82
Minimization with a constraint 88
Minimizing random errors 313
Minimizing sequence 137
Minimizing support 243
Minkowski inquality 68 122
Modulus of continuity 134
Monte-Carlo method 326 327
Moore — Penrose inverse 84
Multi-index 120
Multidimensional integration 321
Multidimensional interpolation 222
Multidimensional splines 265
Multiplicity of interpolation points 280
NAND 9
Natural norm of a matrix 69 70
Negation 8
Newton identity 190
Newton method 338 339
Newton method, multidimensional 343
Newton method, of order two 346
Newton method, two step 346
Newton — Raphson method 340
Newton, Isaac 189
Nomogram 6
Nonlinear approximation 157
NOR 9
Norm 68
Norm bound 72
Norm bound of matrices 69
Norm of an operator 124
Norm, strict 119
Normal equation 87 161 174
Normal matrix 92
Normed element 118
Normed linear space 118
Normed vector space 68
Number representation in arbitrary bases 2
Numerical singularity 53
Numerical stability 17 22
Objective function 372
Octal form 12
Octal system 4 5 11
Odhner, Willgodt Theophil 7
| One-sided derivative 206
ONS 162
ONS of trigonometric functions 169
Operator 123
Optimality of quadrature formulae 311
Optimization problem, linear 371
Optimization problem, semi-infinite 373 374
Optimization problem, standard form of a 375
Order 17
Order "large O" 38
Order "small o" 38
orders of magnitude 10
Orthogonality condition 297
Orthogonality relation in  179
Orthonormal basis of an eigenspace 80
Orthonormal polynomials 165
Orthonormalization method of E. Schmidt 162
Output 30 34 40 41
Over-relaxation 362 363
Overflow 11 13 25
Parallel computation 45 60
Parallelogramm law 125
Parseval equation 163
Partial adder 9
Pascal 36
Pascal, Blaise 7
Peano error constant 301
Peano kernel 192 277 285
Peano kernel representation 285
Peano, Giuseppe 194
Periodic Bernoulli functions 281
Periodic function 131 310
Permutation matrix 51 52 54
Perturbation lemma 74
Pisa, Leonardo of 342
Pivot element 52 389
Pivot search 52
Pivoting 57
Polya formulae 312
Polyhedron, representation theorem for a 379
Poorly-conditioned matrix 79
Positive definite matrix 61
Positive operator 129
Positive quadrature formula 291
Positivity 120 129
Positivity of the B-splines 244
Power method 105 108
Pre-Hilbert space 120 121
Principal minors 58 61
Principal submatrix 61
Procedure 34
Product integration 309
PROGRAM 35
Projection 87
Property A 366
Proximum 136
Pseudo-inverse 84 86
Pseudo-inverse, effective 88
Pseudo-normal solution 83 84 86
Pseudo-random number 327
QR algorithm 76 110
QR decomposition of Householder 64
Quadrature for periodic functions 310
Quadrature formula, Chebychev 313
Quadrature formula, Chevilliet 288
Quadrature formula, Gauss — Hermite 305
Quadrature formula, Gauss — Laguerre 305
Quadrature formula, Gauss — Legendre 298 304
Quadrature formula, Gauss — Lobatto 302 305
Quadrature formula, Gauss — Radau 302 306
Quadrature formula, Mid-point rule 273 275
Quadrature formula, Milne rule 290
Quadrature formula, Newton — Cotes 286 287
Quadrature formula, optimal 314
Quadrature formula, positive 291 298
Quadrature formula, pulcherrima 286
Quadrature formula, rectangle rules 273 275
Quadrature formula, Sard 316
Quadrature formula, Simpson's rule 282 284
Quadrature formula, symmetric 284 304
Quadrature formula, trapezoidal rule 276
Quadrature formula, unsymmetric 286 305
Raphson, Joseph 340
Rational functions 157
Rayleigh quotient 104 108
Recurrence formula of Euler and Wallis 24
Recursion 18
Recursion formula for derivatives of splines 246
Reduction 108
Reduction to tridiagonal or Hessenberg form 92
Redundant equations 390
Reflection 64
register 9
Regression 176
Regula Falsi 342
Regularization 88
Relative accuracy 14
Relaxation parameter 360
Relaxation parameter, optimal 34
Relaxation, simultaneous 361 362
Residual 77 90 104
Result interval 28
Right-sided approximation of the first derivative 207
Romberg method 288
Root, multiple 340
Roots of polynomials 344
Roundoff 1 13 15
Roundoff error 1 20
Row equilibrated 78
Row exchange 50 51
Row operation 49
Row sum criterion, strong 350
Row sum criterion, weak 352
Row sum norm 70
Runge, Carl David Tolme 180 229
runtime 398
Runtime function 399
Runtime, polynomial 399
Schickard, Wilhelm 6
Schwarz inequality 121
Secant method 341 ff.
Separation of the singularity 308
Set of machine numbers 9
Shannon, C.E. 82
Shift technique 114
Side conditions 372
Significant digit 15
Similarity transformation 93 94 101
Simplex algorithm 391
Simplex algorithm, modified 392
SIMPSON, THOMAS 282
Simultaneous over-relaxation method 362
Simultaneous relaxation method 361
Simultaneous under-relaxation method 362
Singular integrand 308
Singular value 80 82 89
Singular value decomposition 79 ff.
Slack variable 376
Slide rule 6
SOR method 363
Sorting method 45
Spectral norm 70
Spectral radius 70 87
Spectral shift 114
Splines 229 ff. 314
Splines, bicubic 267
Splines, bilinear 266
Splines, blending 258 ff.
Splines, cubic 237 248 250 260
Splines, linear 234 240 247 256
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