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Hammerlin G., Hoffmann K.-H., Schumaker L.L. — Numerical Mathematics
Hammerlin G., Hoffmann K.-H., Schumaker L.L. — Numerical Mathematics

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Название: Numerical Mathematics

Авторы: Hammerlin G., Hoffmann K.-H., Schumaker L.L.

Аннотация:

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 433

Добавлена в каталог: 13.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $\mathbb{R}^{N}$      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
1 2 3
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