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| Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in Fortran 90 |
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| Предметный указатель |
Recurrence relation, primitive polynomials modulo 2 287f.
Recurrence relation, primitive polynomials modulo 2 287f.
Recurrence relation, random number generator 268
Recurrence relation, random number generator 268
Recurrence relation, rational function interpolation 105f. 1043
Recurrence relation, rational function interpolation 105f. 1043
Recurrence relation, recursive doubling 973 977 988 999 1071f. 1073
Recurrence relation, recursive doubling 973 977 988 999 1071f. 1073
Recurrence relation, second order 974f. 1074
Recurrence relation, second order 974f. 1074
Recurrence relation, sequence of trig functions 173
Recurrence relation, sequence of trig functions 173
Recurrence relation, sine function 172 500
Recurrence relation, sine function 172 500
Recurrence relation, spherical harmonics 247
Recurrence relation, spherical harmonics 247
Recurrence relation, stability of 21 173ff. 177 224f. 227f. 232 247 975
Recurrence relation, stability of 21 173ff. 177 224f. 227f. 232 247 975
Recurrence relation, trig functions 572
Recurrence relation, trig functions 572
Recurrence relation, weight of Gaussian quadrature 144f.
Recurrence relation, weight of Gaussian quadrature 144f.
Recursion in Fortran 90 958
Recursion in Fortran 90 958
Recursion in multigrid method 865 1009 1336
Recursion in multigrid method 865 1009 1336
Recursive doubling 973f. 979
Recursive doubling 973f. 979
Recursive doubling, cumulants of polynomial 977 999 1071f.
Recursive doubling, cumulants of polynomial 977 999 1071f.
Recursive doubling, linear recurrences 973 988 1073
Recursive doubling, linear recurrences 973 988 1073
Recursive doubling, tridiagonal systems 976
Recursive doubling, tridiagonal systems 976
RECURSIVE keyword 958 1065 1067
RECURSIVE keyword 958 1065 1067
Recursive Monte Carlo integration 306ff. 1161
Recursive Monte Carlo integration 306ff. 1161
Recursive procedure 2/xiv 958 1065 1067 1166
Recursive procedure 2/xiv 958 1065 1067 1166
Recursive procedure, as parallelization tool 958
Recursive procedure, as parallelization tool 958
Recursive procedure, base case 958
Recursive procedure, base case 958
Recursive procedure, for multigrid method 1009 1336
Recursive procedure, for multigrid method 1009 1336
Recursive procedure, re-entrant 1052
Recursive procedure, re-entrant 1052
Recursive stratified sampling 314ff. 1164ff.
Recursive stratified sampling 314ff. 1164ff.
Red-black see Odd-even ordering
Red-black see Odd-even ordering
Reduction functions 948ff.
Reduction of variance in Monte Carlo integration 299 306ff.
Reduction of variance in Monte Carlo integration 299 306ff.
References (explanation) 4f.
References (explanation) 4f.
References (general bibliography) 916ff. 1359f.
References (general bibliography) 916ff. 1359f.
Reflection formula for gamma function 206
Reflection formula for gamma function 206
Regula falsi (false position) 347ff. 1185f.
Regula falsi (false position) 347ff. 1185f.
Regularity condition 775
Regularity condition 775
Regularization, compared with optimal filtering 801
Regularization, compared with optimal filtering 801
Regularization, constrained linear inversion method 799ff.
Regularization, constrained linear inversion method 799ff.
Regularization, linear 799ff.
Regularization, linear 799ff.
Regularization, nonlinear 813
Regularization, nonlinear 813
Regularization, objective criterion 802
Regularization, objective criterion 802
Regularization, of inverse problems 796ff.
Regularization, of inverse problems 796ff.
Regularization, Phillips — Twomey method 799ff.
Regularization, Phillips — Twomey method 799ff.
Regularization, Tikhonov — Miller 799ff.
Regularization, Tikhonov — Miller 799ff.
Regularization, trade-off curve 799
Regularization, trade-off curve 799
Regularization, two-dimensional 803
Regularization, two-dimensional 803
Regularization, zeroth order 797 (see also Inverse problems)
Regularization, zeroth order 797 (see also Inverse problems)
Regularizing operator 798
Reid, John 2/xiv 2/xvi
Reid, John 2/xiv 2/xvi
Rejection method for random number generator 281f.
Rejection method for random number generator 281f.
Relaxation method, automated allocation of mesh points 774f. 777
Relaxation method, automated allocation of mesh points 774f. 777
Relaxation method, computation of spheroidal harmonics 764ff. 1319ff.
Relaxation method, computation of spheroidal harmonics 764ff. 1319ff.
Relaxation method, elliptic partial differential equations 823 854ff. 1332f.
Relaxation method, elliptic partial differential equations 823 854ff. 1332f.
Relaxation method, example 764ff. 1319ff.
Relaxation method, example 764ff. 1319ff.
Relaxation method, for algebraically difficult sets 763
Relaxation method, for algebraically difficult sets 763
Relaxation method, for differential equations 746f. 753ff. 1316ff.
Relaxation method, for differential equations 746f. 753ff. 1316ff.
Relaxation method, Gauss — Seidel method 855 864ff. 876 1338 1341
Relaxation method, Gauss — Seidel method 855 864ff. 876 1338 1341
Relaxation method, internal boundary conditions 775ff.
Relaxation method, internal boundary conditions 775ff.
Relaxation method, internal singular points 775ff.
Relaxation method, internal singular points 775ff.
Relaxation method, Jacobi’s method 855f. 864
Relaxation method, Jacobi’s method 855f. 864
Relaxation method, successive over-relaxation (SOR) 857ff. 862 866 1332f.
Relaxation method, successive over-relaxation (SOR) 857ff. 862 866 1332f.
Remes algorithms, exchange algorithm 553
Remes algorithms, exchange algorithm 553
Remes algorithms, for minimax rational function 199
Remes algorithms, for minimax rational function 199
reshape() intrinsic function 950
reshape() intrinsic function 950
reshape() intrinsic function, communication bottleneck 969
reshape() intrinsic function, communication bottleneck 969
reshape() intrinsic function, order keyword 1050 1246
reshape() intrinsic function, order keyword 1050 1246
Residual 49 54 78
Residual 49 54 78
Residual in multigrid method 863 1338
Residual in multigrid method 863 1338
Resolution function, in Backus — Gilbert method 807
Resolution function, in Backus — Gilbert method 807
Response function 531
Response function 531
Restriction operator 864 1337
RESULT keyword 958 1073
RESULT keyword 958 1073
Reward, $1000 offered 272 1141 1150f.
Reward, $1000 offered 272 1141 1150f.
Richardson’s deferred approach to the limit 134 137 182 702 718ff. 726 788 869
Richardson’s deferred approach to the limit 134 137 182 702 718ff. 726 788 869
Richtmyer artificial viscosity 837
Richtmyer artificial viscosity 837
Ridders’ method, for numerical derivatives 182 1075
Ridders’ method, for numerical derivatives 182 1075
Ridders’ method, root finding 341 349 351 1187
Ridders’ method, root finding 341 349 351 1187
Riemann shock problem 837
Riemann shock problem 837
Right eigenvalues and eigenvectors 451
Right eigenvalues and eigenvectors 451
Rise/fall time 548f.
| Rise/fall time 548f.
Robust estimation 653 694ff. 700 1294
Robust estimation 653 694ff. 700 1294
Robust estimation, Andrew’s sine 697
Robust estimation, Andrew’s sine 697
Robust estimation, average deviation 605
Robust estimation, average deviation 605
Robust estimation, double exponential errors 696
Robust estimation, double exponential errors 696
Robust estimation, Kalman filtering 700
Robust estimation, Kalman filtering 700
Robust estimation, Lorentzian errors 696f.
Robust estimation, Lorentzian errors 696f.
Robust estimation, mean absolute deviation 605
Robust estimation, mean absolute deviation 605
Robust estimation, nonparametric correlation 633ff. 1277
Robust estimation, nonparametric correlation 633ff. 1277
Robust estimation, Tukey’s biweight 697
Robust estimation, Tukey’s biweight 697
Robust estimation, use of a priori covariances 700 (see also Statistical tests)
Robust estimation, use of a priori covariances 700 (see also Statistical tests)
Romberg integration 124 134f. 137 182 717 788 1065
Romberg integration 124 134f. 137 182 717 788 1065
Root finding 143 340ff. 1009 1059
Root finding 143 340ff. 1009 1059
Root finding, advanced implementations of Newton’s rule 386
Root finding, advanced implementations of Newton’s rule 386
Root finding, Bairstow’s method 364 370 1193
Root finding, Bairstow’s method 364 370 1193
Root finding, bisection 343 346f. 352f. 359 390 469 698 1184f.
Root finding, bisection 343 346f. 352f. 359 390 469 698 1184f.
Root finding, bracketing of roots 341 343ff. 353f. 362 364 369 1183f.
Root finding, bracketing of roots 341 343ff. 353f. 362 364 369 1183f.
Root finding, Brent’s method 341 349 660f. 1188f. 1286
Root finding, Brent’s method 341 349 660f. 1188f. 1286
Root finding, Broyden’s method 373 382f. 386 1199
Root finding, Broyden’s method 373 382f. 386 1199
Root finding, compared with multidimensional minimization 375
Root finding, compared with multidimensional minimization 375
Root finding, complex analytic functions 364
Root finding, complex analytic functions 364
Root finding, convergence criteria 347 374
Root finding, convergence criteria 347 374
Root finding, deflation of polynomials 362ff. 370f. 1192
Root finding, deflation of polynomials 362ff. 370f. 1192
Root finding, double root 341
Root finding, double root 341
Root finding, eigenvalue methods 368 1193
Root finding, eigenvalue methods 368 1193
Root finding, false position 347ff. 1185f.
Root finding, false position 347ff. 1185f.
Root finding, in complex plane 204
Root finding, in complex plane 204
Root finding, in relaxation method 754 1316
Root finding, in relaxation method 754 1316
Root finding, in shooting method 746 749f. 1314f.
Root finding, in shooting method 746 749f. 1314f.
Root finding, Jenkins — Traub method 369
Root finding, Jenkins — Traub method 369
Root finding, Laguerre’s method 341 366f. 1191f.
Root finding, Laguerre’s method 341 366f. 1191f.
Root finding, Lehmer — Schur algorithm 369
Root finding, Lehmer — Schur algorithm 369
Root finding, Maehly’s procedure 364 371
Root finding, matrix method 368 1193
Root finding, Muller’s method 364 372
Root finding, multiple roots 341
Root finding, multiple roots 341
Root finding, Newton’s rule 143f. 180 341 355ff. 362 364 370 372ff. 376 469 740 749f. 754 787 874 876 911f. 1059 1189 1194 1196 1314ff. 1339 1341 1355f.
Root finding, Newton’s rule 143f. 180 341 355ff. 362 364 370 372ff. 376 469 740 749f. 754 787 874 876 911f. 1059 1189 1194 1196 1314ff. 1339 1341 1355f.
Root finding, pathological cases 343 356 362 372
Root finding, pathological cases 343 356 362 372
Root finding, polynomials 341 362ff. 449 1191f.
Root finding, polynomials 341 362ff. 449 1191f.
Root finding, Ridders’ method 341 349 351 1187
Root finding, Ridders’ method 341 349 351 1187
Root finding, root-polishing 356 363ff. 369ff. 1193
Root finding, root-polishing 356 363ff. 369ff. 1193
Root finding, safe Newton’s rule 359 1190
Root finding, safe Newton’s rule 359 1190
Root finding, secant method 347ff. 358 364 399 1186f.
Root finding, secant method 347ff. 358 364 399 1186f.
Root finding, singular Jacobian in Newton’s rule 386
Root finding, singular Jacobian in Newton’s rule 386
Root finding, stopping criterion for polynomials 366
Root finding, stopping criterion for polynomials 366
Root finding, use of minimum finding 341
Root finding, use of minimum finding 341
Root finding, using derivatives 355ff 1189
Root finding, using derivatives 355ff 1189
Root finding, without derivatives 354
Root finding, without derivatives 354
Root finding, zero suppression 372 (see also Roots)
Root finding, zero suppression 372 (see also Roots)
Root polishing 356 363ff. 369ff. 1193
Root polishing 356 363ff. 369ff. 1193
Roots, Chebyshev polynomials 184
Roots, Chebyshev polynomials 184
Roots, complex  th root of unity 999f. 1379
Roots, complex th root of unity 999f. 1379
Roots, cubic equations 179f.
Roots, cubic equations 179f.
Roots, Hermite polynomials, approximate 1062
Roots, Hermite polynomials, approximate 1062
Roots, Jacobi polynomials, approximate 1064
Roots, Jacobi polynomials, approximate 1064
Roots, Laguerre polynomials, approximate 1061
Roots, Laguerre polynomials, approximate 1061
Roots, multiple 341 364ff. 1192
Roots, multiple 341 364ff. 1192
Roots, nonlinear equations 340ff.
Roots, nonlinear equations 340ff.
Roots, polynomials 341 362ff. 449 1191f.
Roots, polynomials 341 362ff. 449 1191f.
Roots, quadratic equations 178
Roots, quadratic equations 178
Roots, reflection in unit circle 560 1257
Roots, reflection in unit circle 560 1257
Roots, square, multiple precision 912 1356
Roots, square, multiple precision 912 1356
Rosenbrock method 730 1308
Rosenbrock method 730 1308
Rosenbrock method, compared with semi-implicit extrapolation 739
Rosenbrock method, compared with semi-implicit extrapolation 739
Rosenbrock method, stepsize control 731 1308f.
Rosenbrock method, stepsize control 731 1308f.
Roundoff error 20 881 1362
Roundoff error, bracketing a minimum 399
Roundoff error, compile time vs. run time 1012
Roundoff error, conjugate gradient method 824
Roundoff error, eigensystems 458 467 470 473 476 479 483
Roundoff error, eigensystems 458 467 470 473 476 479 483
Roundoff error, extended trapezoidal rule 132
Roundoff error, extended trapezoidal rule 132
Roundoff error, general linear least squares 668 672
Roundoff error, general linear least squares 668 672
Roundoff error, graceful 883 1343
Roundoff error, graceful 883 1343
Roundoff error, hardware aspects 882 1343
Roundoff error, hardware aspects 882 1343
Roundoff error, Householder reduction 466
Roundoff error, Householder reduction 466
Roundoff error, IEEE standard 882f. 1343
Roundoff error, IEEE standard 882f. 1343
Roundoff error, interpolation 100
Roundoff error, interpolation 100
Roundoff error, least squares fitting 658 668
Roundoff error, least squares fitting 658 668
Roundoff error, Levenberg — Marquardt method 679
Roundoff error, Levenberg — Marquardt method 679
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