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Henrici P. — Elements of numerical analysis
Henrici P. — Elements of numerical analysis

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Название: Elements of numerical analysis

Автор: Henrici P.

Язык: en

Рубрика: Математика/Численные методы/Численный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1964

Количество страниц: 328

Добавлена в каталог: 23.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute value, of complex number      21
Adams — Bashforth method      276 ff 283 285 318
Adams — Moulton method      280 ff 318
Aitken’s $A^2$-method      72 ff 151 174 237
Aitken’s Lemma      204
Algebra, fundamental theorem of      34
Algol      9
Algorithm      4
Algorithm, stable      314
Argument, of complex number      21
Asymptotic expansion      239
Averaging operator      225
Bairstow’s method      110 ff 176
Base, of number system      291
Basic unit      301
Bernoulli’s method      146 ff.
Bernoulli’s method, stability of      320
Bessel function      177 f 189 190 203 211 223 229 230 235 237 258
Bessel’s interpolation formula      226 235 249
Binomial coefficients      26 40 52 56 140 142 204 214 253 308 320
Binomial theorem      41 140
Binomial theorem, generalized      251
Bolzano — Weierstrass, theorem of      5
CDC 1604 computer      297
Chebyshev polynomials      124 144 194
Circular frequency      160
Complex conjugate number      24
Complex number      14
Complex number, root of      27
Complex plane      18
Constructive method      3 264
Continued fraction      177
Continuity, uniform      193
Contracting map      99
Convergence of algorithm      9
Convergence, acceleration of      10 70 116 149 152 174 237 243 259 272
Convergence, linear      75 104
Convergence, quadratic      76 103
Conversion, of binary numbers      292 ff.
Corrector formula      281
Cramer’s Rule      107
Dedekind section      6 169
Deflation      86 162
Derivative of polynomial      40
Derivative of polynomial, evaluation of      54
Derivative, total      266
Determinant, Wronskian      125 f 129 133 ff.
Difference equation, homogeneous      49 f 50 135
Difference equation, linear      48 119 284 310
Difference equation, non-linear      243 282
Difference operator, backward      141
Difference operator, central      225
Difference operator, forward      72 214
Difference table      142 304
Differences, accumulation of error in      302
Differences, backward      248
Differences, central      249 285
Differential equation      44 263
Differential equation, numerical solution of      263 ff.
Differential equation, numerical solution of, by methods based on integration      276 ff.
Differential equation, numerical solution of, by methods based on Taylor’s formula      267 ff.
Differential equation, numerical solution of, propagation of error in      317
Differential equation, solution of      263
Differentiation operator, basic      235
Discretization error      286
End correction, in trapezoidal formula      257
Error terms, oscillatory      286
Error, asymptotic formula for      10
Error, bound for      10
Euler method      267 318
Euler — Cauchy method      267
Everett’s interpolation formula      226
Expected value of random variable      306
Exponent, of floating number      299
Exponential function, definition of      31
Extrapolation to the limit      239 f 271 288
Fibonacci sequence      127 148 164 319
Fixed point arithmetic      297
Fixed point, of iteration      63
Floating point arithmetic      299 312
FORTRAN      9 300
Fraction, binary      293
Function, analytic      261
Function, domain of      30
Function, periodic, integration of      259
Function, range of      30
Function, sufficiently differentiable      265
Gaussian quadrature      255 262
Gauss’ backward formula      223
Gauss’ forward formula      223
Generating function      251
Graeffe’s method      161
Horner’s scheme      51 85 316 321
IBM 1620 computer      297
IBM 7090 computer      297 299
Imaginary part of complex number      15
Imaginary unit      13
Incremental form, of numerical formula      88
Influence coefficients      311
Initial value problem for difference equation      48
Initial value problem for differential equation      264
Instability, numerical      see “Stability numerical”
Interpolating polynomial      183 ff.
Interpolating polynomial, error of      186
Interpolating polynomial, existence of      183
Interpolating polynomial, finalized      218
Interpolating polynomial, representation of      201 207 208 221 223 225 226
Interpolating polynomials, sequences of      191
Interpolation coefficients for Everett interpolation      227
Interpolation coefficients for Lagrangian interpolation      184
Interpolation coefficients for Lagrangian interpolation, normalized      201
Interpolation, inverse      209 ff.
Iteration      61 ff.
Iteration method, convergence of, for functions of one variable      65
Iteration method, convergence of, for functions of several variables      99
Iteration, inner      282
Iteration, propagation of error in      313
Jacobian matrix      104
Kepler’s equation      67 68 70 92
Lagrangian interpolation coefficients      184
Lagrangian interpolation coefficients, normalized      201
Legendre function      253
Leibnitz formula, for differentiation of product      42
linear combination      130
Linear dependence      128 136
Lipschitz condition      63 100 265 270 282
Lipschitz constant      63 101 270 278 282 283
Lipschitz constant, bound for      64 101
Logarithms, calculation of      242
Loss of accuracy      243
L’Hopital’s Rule      186 188
Machine number      297 313
Mantissa, of floating number      299
Mean value theorem      64 70 75 80 94 188 310
Midpoint formula      251 285 318
Midpoint formula, applied to differential equations      319
Midpoint value      260
Missing entry in table      192
Modulus of complex number      21
Moivre’s formula      26
Muller’s method      88 194 212
Multiple precision      301
nabla      141
Neville’s algorithm      207 ff.
Newton — Cotes formulas      255
Newton’s backward formula      223 248 276
Newton’s forward formula      223 254
Newton’s method      76 ff 175
Newton’s method for systems of equations      105 ff.
Newton’s method, applied to polynomials      84
Newton’s method, non-local convergence theorem for      79
Norm, of vector      98
Normal probability distribution      306
Number system      291
Number system, binary      292
Numerical analysis, definition of      3
Numerical differentiation      231 ff 242 245
Numerical differentiation for equidistant abscissas      233
Numerical differentiation, error of      232
Numerical integration      246 ff.
Numerical integration over extended intervals      254
Numerical integration, error of      247
Numerical integration, using backward differences      248
Numerical integration, using central differences      249
Operator, linear      120
Overflow      297
Pascal’s triangle      53
Polar representation of complex number      22
Polynomial      33
Polynomial equation      6
Polynomial, approximation of, by polynomial of lower degree      193 ff.
Polynomial, characteristic      121
Polynomial, degree of      33
Polynomial, leading coefficient of      33
Polynomial, real      33 38
Polynomial, representation by linear factors      35
Polynomial, zero of      34
Predictor formula      281
Quadratic factors      39
Quadratic factors, determination of      108 ff.
Quotient-difference algorithm      162 ff.
Quotient-Difference algorithm, computational checks for      174
Quotient-Difference algorithm, convergence theorems for      166
Quotient-difference algorithm, progressive form of      170
Random variables      12 305
Random variables, independent      307
Range of function      30
Range of machine      297
Real part of complex number      15
Regula Falsi      87 213
Representation, correctly rounded      297
Rhombus rules      163
Rolle’s Theorem      187 224
Romberg integration      255 259
Roots of unity      28 37
Rounding      10 302
Rounding error      169
Rounding error, accumulated      302 309
Rounding error, local      302
Rounding error, local, definition of      309
Runge — Kutta method, classical      275 277 281
Runge — Kutta method, simplified      274
Runge — Kutta — Taylor method      275
Scaling      298
Schwarz inequality      101 f.
Sequence of real numbers      46
Sequence of vectors      99
Sequence, monotonic      80 94
Sign waves      158
Simpson’s rule      251 287
Simpson’s rule, applied to differential equations      319 f.
Solution of difference equation      46 f.
Solution of differential equation      44 f.
Solution of equation      62
Solution, general      122 f.
Solution, particular      131 ff.
Solution, trivial      121
Square root, computation of, by Newton’s method      81
Stability of solutions of difference equations      128
Stability, numerical      11 168 302 314
Stability, numerical, of methods for solving differential equations      283 ff 317
Stability, numerical, of numerical differentiation      242
Stability, numerical, of quotient-difference algorithm      169
Standard deviation      306 f.
Starting error      277 279 286
Starting method      278
Statistical theory of rounding      305
Steffensen iteration for single equations      91
Steffensen iteration for systems      115
Stirling’s formula form      192 308
Stirling’s interpolation formula      225 233 250
Stochastic model of rounding      305
Sum, evaluation of      312
Table, well interpolable      190
Taylor algorithm      267 270 271 272
Taylor expansion for solving differential equations      265
Taylor expansion of polynomial      54
Taylor’s Formula      270 272
Theorem, role of, in numerical analysis      10
Throwback      227 ff.
Trapezoidal rule      250 255 259
Trapezoidal rule with end correction      255
Trapezoidal value of integral      256 260
Triangle inequality      24 99
Variance of random variable      307
Variation of constants      49 133
Vector notation      98
Weierstrass, theorem of, on polynomial approximation      192
Whittaker’s method      87
Zero, of polynomial      34
Zero, of polynomial, dominant      146
Zero, of polynomial, multiplicity of      36
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