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| Conte S.D., de Boor C. — Elementary numerical analysis - an algorithmic approach |
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| Предметный указатель |
Multiplicity of a zero 36
Multistep methods 373ff
Murnaghan — Wrench algorithm 241
Nested form of a polynomial 33
Nested multiplication 112
Nested multiplication for Chebyshev polynomials 258
Nested multiplication for Newton form 33 112
Nested multiplication for orthogonal polynomials 257
Nested multiplication for series 37
Nested multiplication in fast Fourier transform 279
Neville’s algorithm 50
Newton backward-difference formula 62 373 382
Newton form of a polynomial 32ff
Newton formula for the interpolating polynomial 40—41
Newton formula for the interpolating polynomial, algorithm for calculation of coefficients 44
Newton formula for the interpolating polynomial, program 45 68—69
Newton forward-difference formula 57
Newton’s method 79 100—102 104—106 108 113ff 241 244 404
Newton’s method for systems 216—222 223 224
Newton’s method for systems, algorithm 217
Newton’s method for systems, damped 218—220
Newton’s method for systems, modified 221
Newton’s method for systems, quasi- 223
Newton’s method, algorithm 79
Newton’s method, algorithm for finding real zeros of polynomials 113
Newton’s method, algorithm for finding real zeros of polynomials, program 115
Node of a rale 295
Noise 295
Norm 170ff
Norm, Euclidean 171
Norm, function 235
Norm, matrix 172
Norm, max 171
Norm, vector 171
Normal equations for least-squares problem 215 248—251 260
Normalized floating-point number 7
Numerical differentiation 290 295—303
Numerical instability see “Instability”
Numerical integration see “Integration”
Numerical quadrature see “Integration”
Octal system 3
One-step methods 355
Optimization 209ff
Optimum step size in differentiation 301
Optimum step size in solving differential equations 366—372 385 396
Order of a root 36 109 110
Order of a trigonometric polynomial 268
Order of convergence 20—24 102
Order, symbol  20—24 163 192 202 221 337ff 353ff 361 363—365 367 390 393
Order, symbol o( ) 20—24 98 334ff
Orthogonal functions 250 252 270 418
Orthogonal polynomials 251ff 313
Orthogonal polynomials, generation of 261—265
Orthogonal projection 248
Osculatory interpolation 62ff 308
Osculatory interpolation, program 68—69
Overflow 8
Parseval’s relation 270
Partial double precision accumulation 3
Partial pivoting 159
Permutation 143
Piecewise-cubic interpolation 285ff
Piecewise-cubic interpolation, programs 285 287 290
Piecewise-parabolic 293
Piecewise-polynomial functions 284ff 319 418
Piecewise-polynomial interpolation 284ff
Pivotal equation in elimination 151
Pivoting strategy in elimination 157 180
Polar form of a complex number 270 277 351
Polynomial equations 110ff
Polynomial equations, complex roots 120ff
Polynomial equations, real roots 110ff
Polynomial forms, Lagrange 38
Polynomial forms, nested 33
Polynomial forms, Newton 32ff
Polynomial forms, power 32
Polynomial forms, shifted power 32
Polynomial interpolation see “Interpolating polynomial”
Polynomials, algebraic 31ff
Polynomials, trigonometric 268ff
Port 421
Power form of a polynomial 32
Power method 192—196
Power spectrum 271
Predictor-corrector methods 379ff
Propagation of errors 14 395
QR method 199—200
Quadratic convergence 100ff
Quadratic formula 13—14
Quotient polynomial 35
Rayleigh quotient 201
Real numbers 24
Rectangle rale 305
Rectangle rale, composite 320
Reduced or deflated polynomial 117
| Regula Falsi 76
Regula falsi, modified see “Modified regula falsi”
Relative error 12
Relaxation 232—233
Remez algorithm 241
Residual 169
Rolle’s Theorem 26 52 74
Romberg integration 340—345
Romberg integration, program 343—344
Round-off error 8
Round-off error in differentiation 300—302
Round-off error in integration 322
Round-off error in solving differential equations 395—398
Round-off error in solving equations 83 87 116—117
Round-off error in solving linear systems 157 178—185
Round-off error, propagation of 9ff 12ff 395ff
Rounding 8
Rule 295
Runge — Kutta methods 362ff
Runge — Kutta methods, Fehlberg 369—370
Runge — Kutta methods, order 2 363—364
Runge — Kutta methods, order 4 364
Runge — Kutta methods, Verner 370
Sampling frequency 272
Scalar (or inner) product 142 143
Scalar (or inner) product of functions 251 270 273
Schur’s Theorem 197 234
Secant method 78—79 102—104 106—109 412
Secant method, algorithm 78
Self-starting 365 376
SEQUENCE 20
Series summation 37
Shooting methods 412ff
Significant digits 12
Significant-digit arithmetic 18
Similarity transformation 196ff
Similarity transformation into upper Hessenberg form 197—199
Similarity transformation into upper Hessenberg form, algorithm 199
Simpson’s rale 307 317 318 329—332 385
Simpson’s rale, composite 320
Simpson’s rale, program 325
Simultaneous displacement see “Jacobi iteration”
Single precision 7
Smoothing 271
SOR 231
Spectral radius 228
Spectrum of a matrix see “Eigenvalues”
Spectrum of a periodic function 271
SPLINE 289—293
Stability see “Instability”
Stable, absolutely 394
Stable, relatively 394
Stable, strongly 391 392
Stable, weakly 393
Steepest descent 210ff.
Steepest descent, algorithm 211
Steffensen iteration 98 108
Steffensen iteration, algorithm 98
Step-size control 366 384 394
Sturm sequence 205
Successive displacement see “Gauss — Seidel iteration”
Successive overrelaxation (SOR) 231
Synthetic division by a linear polynomial 35
Tabulated function 55
Taylor polynomial 37 63 64
Taylor series, truncated 27 32 100 336 353 354 357 359 390
Taylor series, truncated for functions of several variables 29 216 363 414
Taylor’s algorithm 354ff 362 366
Taylor’s formula with (integral) remainder 27 (see also “Taylor series truncated”)
Termination criterion 81 85 122 194 227
Three-term recurrence relation 254
Total pivoting 159
Trace of a matrix 146
Trapezoid rale 272 305 317 340
Trapezoid rale, composite 32 1
Trapezoid rale, corrected see “Corrected trapezoid rale”
Trapezoid rale, program 323
Triangle inequality 171 176
Triangular factorization 160ff
Triangular factorization, program 165—166
Tridiagonal matrix see “Matrix tridiagonal”
Trigonometric polynomial 268ff
Truncation error see “Discretization error”
Two-point boundary value problems 406ff
Underflow 8
Unit roundoff 9
Unit vector 135
Unstable see “Instability”
Upper-triangular 131 147—149
Vandermonde matrix 147
Vector 129
Wagon wheels 274
Waltz 106
Wavelength 271
wronskian 347
Zeitgeist 432
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