|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Henrici P. — Elements of numerical analysis |
|
|
|
| Предметный указатель |
Absolute value, of complex number 21
Adams — Bashforth method 276 ff 283 285 318
Adams — Moulton method 280 ff 318
Aitken’s  -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
|
|
|
| Реклама |
|
|
|
|
|
О проекте