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| Авторизация |
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| Burden R.L., Faires J.D. — Numerical analysis |
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| Предметный указатель |
Operation counts, Cramer's rule 362
Operation counts, factorization 371
Operation counts, fast Fourier transform 488
Operation counts, Gauss — Jordan 336
Operation counts, Gaussian elimination 332
Operation counts, scaled column pivoting 343
Operation counts, systems 355
Organ problem 656
Orthogonal matrix 500
Orthogonal set of functions 454
Orthogonal set of vectors 499
Orthonormal set of functions 454
Orthonormal set of vectors 499
Osculating polynomial 123
Ostrowski — Reich theorem 418
Over-relaxation method 416
Overflow 14
Pade approximation technique 470
Pade Rational' Approximation Algorithm 471
Parabolic partial-differential equation 624 635
Parametric curve 148
Partial pivoting 340 see
Partial-differential equation definition 622
Partial-differential equation, elliptic 623 625
Partial-differential equation, finite element method 657
Partial-differential equation, hyperbolic 624 649
Partial-differential equation, parabolic 624 635
Pendulum problem 232 303
Permutation matrix 367
Persymmetric matrix 505
Perturbed problem 236
Petroleum reservoir problem 649
Picard method 238
Piecewise cubic Hermite polynomial 150
Piecewise linear basis functions 607
Piecewise Linear Rayleigh — Ritz Algorithm 610
Piecewise polynomial approximation 131
Pipe organ problem 656
Pivot element 329
Pivoting, complete 344
Pivoting, maximal 344
Pivoting, maximal column 340
Pivoting, scaled column 342
Pivoting, strategies 344
Plate sinkage problem 543 560
Poisson equation 623
Poisson Equation Finite-Difference Algorithm 630
Polynomial definition 82
Polynomial evaluation 20 83
Polynomial, algebraic 96
Polynomial, Bernstein 111
Polynomial, characteristic 309 401
Polynomial, Chebyshev 91 459
Polynomial, Hermite 91 123
Polynomial, interpolating 98
Polynomial, Lagrange 98
Polynomial, Laguerre 91 229 459
Polynomial, Legendre 207 457
Polynomial, Maclaurin 8
Polynomial, monic 462
Polynomial, nested 20
Polynomial, Newton 113
Polynomial, osculating 123
Polynomial, roots of 82
Polynomial, Taylor 8 97 255
Polynomial, trigonometric 455 480 485
Population growth, Gompertz 68
Population growth, logistic 294
Population problems 39 67 95 110 121 145
Positive definite matrix 373 423 502
Power method 506
Power Method Algorithm 508
Power method for symmetric matrices 511
Power series, economization of 466
Precision, degree of 179
Predator-prey problem 303
Predictor-corrector algorithm 284
Predictor-corrector method 278
Program, general-purpose 32
Program, special-purpose 32
Pseudocode 24
QR algorithm 534
QR method 530
Quadratic convergence 70 72 81 554
Quadratic formula 18
Quadratic spline 132 144
Quadrature, Gaussian 205 214
Quasi-Newton method 561
Racquetball problem 68
Rate of convergence 29
Rational function approximation 469
Rayleigh — Ritz method 605
Reduced form, system of equations 325
Region of absolute stability 317
Regula falsi method 63
Relative error 15
Relaxation method 416
Remainder term 8
Residual vector 414 424
Reverse shooting method 583
Richardson extrapolation 168 596 602
Richardson method 642
Riemann integral 5
Rolle's theorem 4
Romberg algorithm 202
Romberg algorithm, cautious 203
Romberg integration 199
Root definition 40
Root finding, bisection method 40
Root finding, method of false position 63
Root finding, Mueller's method 87
Root finding, Newton's method 56
Root finding, Newton's method for systems 555
Root finding, secant method 61
Root, condition 311
Root, multiple 73
Root, simple 74
Rotation matrix 531
Round-off error 13 15
Rounding arithmetic 15
Row vector 326
Ruddy duck problem 139
Runge — Kutta for Systems of Differential Equations Algorithm 297
Runge — Kutta method 254
Runge — Kutta Order Four Algorithm 259
| Runge — Kutta order two method 257
Runge — Kutta — Fehlberg algorithm 266
Runge — Kutta — Fehlberg method 265
Runge — Kutta — Verner method 269
Scalar product 346
Scaled-column pivoting 342
Schur theorem 501
Secant Algorithm 62
Secant method definition 61
Secant method for stiff equation 318
Secant method, for nonlinear boundary-value problem 587
Secant method, order of convergence 78
Sequence, limit of 2
Series, Fourier 455
Series, Maclaurin 8
Series, Taylor 8
Set, convex 235
Sherman — Morrison formula 562
Shooting method, linear equation 580
Shooting method, nonlinear equation 585
Similar matrices 500
Similarity transformation 501
Simpson's composite rule 186
Simpson's Double Integral Algorithm 217
Simpson's method 280
Simpson's rule 175
Simpson's three-eighths rule 180
Singular matrix 349
Slap 434
SOR Algorithm 418
SOR method definition 416
SOR method in heat equation 640
SOR method in Poisson equation 632
Sparse matrix 390
SPARSPAK 434
Spectral radius definition 403
Spectral radius, relation to convergence 404
Speed and distance problem 130 145
Spread of contagious disease 269
Spring-mass problem 199
Square matrix 348
Stable algorithm 26
Stable method 189 305
Steady-state heat distribution 623
Steepest descent algorithm 570
Steepest descent method 568
Steffensen Algorithm 80
Steffensen method, quadratic convergence 81
Stein — Rosenberg theorem 414
Step size 239
Stiff differential equation 314
Stirling formula 118
Strictly diagonally dominant matrix 371
Strongly stable method 311
Sturm — Liouville system 497
SubMatrix 358
Submatrix, leading principal 370
Successive Over Relaxation (SOR) Algorithm 418
Successive over relaxation (SOR) method 416
Superlinear convergence 82 561
Surface area 223
Symmetric matrix 353
Symmetric Power Method Algorithm 511
Synthetic division 84
System of differential equations 233 294
System of linear equations 325
Taylor method for initial-value problem 249
Taylor polynomial 8 97
Taylor polynomial in two variables 255
Taylor series 8
Taylor's theorem 8 255
Terrain vehicles problem 68
Test equation 315
Three-point formula 161
Total pivoting 344
Transformation matrix, Gauss 363
Transmission line problem 657
Transpose matrix 353
Trapezium rule see "Trapezoidal rule"
Trapezoidal method 248 317
Trapezoidal rule 175
Trapezoidal rule, composite 187
Trapezoidal with Newton Iteration Algorithm 318
Triangular system of equations 325
Tridiagonal matrix definition 379
Tridiagonal matrix, block 384
Tridiagonal matrix, reduction to 523
Trigonometric polynomial approximation 455 480 485
Triple integral 219
Truncation error 8
Two-point boundary-value problem 578
Unconditionally stable 639 642
Under-relaxation method 416
Underflow 14
Unitary matrix 501
Unstable algorithm 26
Unstable method 165 311
Upper Hessenberg matrix 529 537
Upper triangular matrix 348 362
van der Pol equation 591
Variable step-size muLtistep method 282
Variational property 605
Vector definition 326
Vector space 346
Vector, convergence 394
Vector, norm of 390
Vector, orthogonal set 454 499
Vector, orthonormal set 454 499
vibrating beam 497
Vibrating string 624
Wave equation 624
Wave Equation Finite-Difference Algorithm 652
Weakly stable method 311
Weierstrass approximation theorem 96
Weight function 453
Weighted Mean Value Theorem for Integrals 6
Well-conditioned matrix 426
Well-posed problem 236
Wielandt's Deflation Algorithm 518
Zero matrix 348
Zero polynomial 82
Zero, definition 40
Zero, multiplicity of 73
Zero, simple 74
Zeroth divided difference 112
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