|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in FORTRAN77 |
|
|
|
| Предметный указатель |
Recurrence relation, spherical harmonics 247
Recurrence relation, stability of 21 173ff. 177 224f. 227f. 232 247 975
Recurrence relation, trig functions 572
Recurrence relation, weight of Gaussian quadrature 144f.
Recursion in Fortran 90 958
Recursion in multigrid method 865 1009 1336
Recursive doubling 973f. 979
Recursive doubling cumulants of polynomial 977 999 1071f.
Recursive doubling linear recurrences 973 988 1073
Recursive doubling tridiagonal systems 976
RECURSIVE keyword 958 1065 1067
Recursive Monte Carlo integration 306ff. 1161
Recursive procedure 2/xiv 958 1065 1067 1166
Recursive procedure as parallelization tool 958
Recursive procedure base case 958
Recursive procedure for multigrid method 1009 1336
Recursive procedure re-entrant 1052
Recursive stratified sampling 314ff. 1164ff.
Red — black see “Odd-even ordering”
Reduction functions 948ff.
Reduction of variance in Monte Carlo integration 299 306ff.
References (explanation) 4f.
References (general bibliography) 916ff. 1359f.
Reflection formula for gamma function 206
Regula falsi (false position) 347ff. 1185f.
Regularity condition 775
Regularization compared with optimal filtering 801
Regularization constrained linear inversion method 799ff.
Regularization linear 799ff.
Regularization nonlinear 813
Regularization objective criterion 802
Regularization of inverse problems 796ff.
Regularization Phillips — Twomey method 799ff.
Regularization Tikhonov — Miller 799ff.
Regularization trade-off curve 799
Regularization two-dimensional 803
Regularization zeroth order 797 (see also “Inverse problems”)
Regularizing operator 798
Reid, John 2/xiv 2/xvi
Rejection method for random number generator 281ff.
Relaxation method automated allocation of mesh points 774f. 777
Relaxation method computation of spheroidal harmonics 764ff. 1319ff.
Relaxation method elliptic partial differential equations 823 854ff. 1332f.
Relaxation method example 764ff. 1319ff.
Relaxation method for algebraically difficult sets 763
Relaxation method for differential equations 746f. 753ff. 1316ff.
Relaxation method Gauss — Seidel method 855 864ff. 876 1338 1341
Relaxation method internal boundary conditions 775ff.
Relaxation method internal singular points 775ff.
Relaxation method Jacobi’s method 855f. 864
Relaxation method successive over-relaxation (SOR) 857ff. 862 866 1332f.
Remes algorithms communication bottleneck 969
Remes algorithms exchange algorithm 553
Remes algorithms for minimax rational function 199
Remes algorithms order keyword 1050 1246
Remes algorithms reshape() intrinsic function 950
Residual 49 54 78
Residual in multigrid method 863 1338
Resolution function, in Backus — Gilbert method 807
Response function 531
Restriction operator 864 1337
RESULT keyword 958 1073
Reward, $1000 offered 272 1141 1150f.
Richardson’s deferred approach to the limit 134 137 182 702 718ff. 726 788 869
Richtmyer artificial viscosity 837
Ridders’ method, for numerical derivatives 182 1075
Ridders’ method, root finding 341 349 351 1187
Riemann shock problem 837
Right eigenvalues and eigenvectors 451
Rise/fall time 548f.
Robust estimation 653 694ff. 700 1294
Robust estimation Andrew’s sine 697
Robust estimation average deviation 605
Robust estimation double exponential errors 696
Robust estimation Kalman filtering 700
Robust estimation Lorentzian errors 696f.
Robust estimation mean absolute deviation 605
Robust estimation nonparametric correlation 633ff. 1277
Robust estimation Tukey’s biweight 697
Robust estimation use of a priori covariances 700 (see also “Statistical tests”)
Romberg integration 124 134f. 137 182 717 788 1054f. 1065
Root finding 143 340ff. 1009 1059
Root finding advanced implementations of Newton’s rule 386
Root finding Bairstow’s method 364 370 1193
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 Brent’s method 341 349 660f. 1188f. 1286
Root finding Broyden’s method 373 382f. 386 1199
Root finding compared with multidimensional minimization 375
Root finding complex analytic functions 364
Root finding convergence criteria 347 374
Root finding deflation of polynomials 362ff. 370f. 1192
Root finding double root 341
Root finding eigenvalue methods 368 1193
Root finding false position 347ff. 1185f.
Root finding in complex plane 204
Root finding in relaxation method 754 1316
Root finding in shooting method 746 749f. 1314f.
Root finding Jenkins — Traub method 369
Root finding Laguerre’s method 341 366f. 1191f.
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 Newton’s rule 143f. 180 341 355ff. 362 364 370 372ff. 376 469 740 749f. 754 787 874 876 91If. 1059 1189 1194 1196 1314ff. 1339 1341 1355f.
Root finding polynomials 341 362ff. 449 1191f.
Root finding Ridders’method 341 349 351 1187
Root finding Root finding pathological cases 343 356 362 372
Root finding root — polishing 356 363ff. 369ff. 1193
Root finding safe Newton’s rule 359 1190
Root finding secant method 347ff. 358 364 399 1186f.
Root finding singular Jacobian in Newton’s rule 386
Root finding stopping criterion for polynomials 366
Root finding use of minimum finding 341
Root finding using derivatives 355ff. 1189
Root finding without derivatives 354
Root finding zero suppression 372 (see also “Roots”)
Root polishing 356 363ff. 369ff. 1193
Roots Chebyshev polynomials 184
Roots complex nth root of unity 999f. 1379
Roots cubic equations 179f.
Roots Hermite polynomials, approximate 1062
Roots Jacobi polynomials, approximate 1064
Roots Laguerre polynomials, approximate 1061
Roots multiple 341 364ff. 1192
Roots nonlinear equations 340ff.
Roots polynomials 341 362ff. 449 1191f.
Roots quadratic equations 178
Roots reflection in unit circle 560 1257
Roots square, multiple precision 912 1356
Rosenbrock method 730 1308
Rosenbrock method compared with semi-implicit extrapolation 739
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 extended trapezoidal rule 132
Roundoff error general linear least squares 668 672
Roundoff error graceful 883 1343
Roundoff error hardware aspects 882 1343
Roundoff error Householder reduction 466
Roundoff error IEEE standard 882f. 1343
Roundoff error interpolation 100
Roundoff error least squares fitting 658 668
Roundoff error Levenberg — Marquardt method 679
Roundoff error linear algebraic equations 23 27 29 47 56 84 1022
Roundoff error linear predictive coding (LPC) 564
| Roundoff error magnification of 20 47 1022
Roundoff error maximum entropy method (MEM) 567
Roundoff error measuring 88If. 1343
Roundoff error multidimensional minimization 418 422
Roundoff error multiple roots 362
Roundoff error numerical derivatives 180f.
Roundoff error recurrence relations 173
Roundoff error reduction to Hessenberg form 479
Roundoff error series 164f.
Roundoff error straight line fitting 658
Roundoff error variance 607
Row degeneracy 22
Row operations on matrix 28 31f.
Row totals 624
Row-indexed sparse storage 71f. 1030
Row-indexed sparse storage transpose 73f.
RSS algorithm 314ff. 1164
RST properties (reflexive, symmetric, transitive) 338
Run-length encoding 901
Run-length encoding high-order 1297
Run-length encoding stepsize control 1298f.
Runge — Kutta method 702 704ff. 731 740 1297ff. 1308
Runge — Kutta method Cash — Karp parameters 710 1299f.
Runge — Kutta method embedded 709f. 731 1298 1308
Runge — Kutta method high-order 705
Runge — Kutta method quality control 722
Runge — Kutta method stepsize control 708ff.
Rybicki, G.B. 84ff. 114 145 252 522 574 600
S-box for Data Encryption Standard 1148
Sampling importance 306f.
Sampling Latin square or hypercube 305f.
Sampling recursive stratified 314ff. 1164
Sampling stratified 308f.
Sampling theorem 495 543
Sampling theorem for numerical approximation 600ff.
Sampling uneven or irregular 569 648f. 1258
Sande — Tukey FFT algorithm 503
SAVE attribute 953f. 958f. 961 1052 1070 1266 1293
SAVE attribute redundant use of 958f.
SAVE statements 3
Savitzky — Golay filters for data smoothing 644ff. 1283f.
Savitzky — Golay filters for numerical derivatives 183 645
scale() intrinsic function 1107
Scallop loss 548
Scatter — with — combine functions 984 1002f. 1032 1366 1380f.
scatter_add() utility function 984 990 1002 1032
scatter_max() utility function 984 990 1003
Schonfelder, Lawrie 2/xi
Schrage’s algorithm 269
Schrodinger equation 842ff.
Schultz’s method for matrix inverse 49 598
Scope 956ff. 1209 1293 1296
Scoping unit 939
SDLC checksum 890
Searching an ordered table 110f. 1045f.
Searching selection 333 1177f.
Searching with correlated values 111 1046f.
Secant method 341 347ff. 358 364 399 1186f.
Secant method Broyden’s method 382f. 1199f.
Secant method multidimensional (Broyden’s) 373 382f. 1199
Second Euler — Maclaurin summation formula 135f.
Second order differential equations 726 1307
Seed of random number generator 267 1146f.
select case statement 2/xiv 1010 1036
Selection 320 333 1177f.
Selection by packing 1178
Selection by partition — exchange 333 1177f.
Selection find m largest elements 336 1179f.
Selection for median 698 1294
Selection heap algorithm 336 1179
Selection operation count 333
Selection parallel algorithms 1178
Selection timings 336
Selection use to find median 609
Selection without rearrangement 335 1178f.
Semi-implicit Euler method 730 735f.
Semi-implicit extrapolation method 730 735f. 1310f.
Semi-implicit extrapolation method compared with Rosenbrock method 739
Semi-implicit extrapolation method stepsize control 737 131If.
Semi-implicit midpoint rule 735f. 1310f.
Semi-invariants of a distribution 608
Sentinel, in Quicksort 324 333
Separable kernel 785
Separation of variables 246
Serial computing convergence of quadrature 1060
Serial computing random numbers 1141
Serial computing sorting 1167
Serial data port 892
Series 159ff.
Series accelerating convergence of 159ff.
Series alternating 160f. 1070
Series asymptotic 161
Series Bessel function  241
Series Bessel function  235
Series Bessel functions 160 223
Series cosine integral 250
Series divergent 161
Series economization 192f. 195 1080
Series Euler’s transformation 160f. 1070
Series exponential integral 216 218
Series Fresnel integral 248
Series hypergeometric 202 263 1138
Series incomplete beta function 219
Series incomplete gamma function 210 1090f.
Series Laurent 566
Series relation to continued fractions 163f.
Series roundoff error in 164f.
Series sine and cosine integrals 250
Series sine function 160
Series Taylor 355f. 408 702 709 754 759
Series transformation of 160ff. 1070
Series van Wijngaarden’s algorithm 161 1070
Shaft encoder 886
Shakespeare 9
Shampine’s Rosenbrock parameters 732 1308
shape() intrinsic function 938 949
Shell algorithm (Shell’s sort) 321ff. 1168
Sherman — Morrison formula 65ff. 83 382
Shifting of eigenvalues 449 470f. 480
Shockwave 831 837
Shooting method computation of spheroidal harmonics 772 1321ff.
Shooting method example 770ff. 1321ff.
Shooting method for differential equations 746 749ff. 770ff. 1314ff. 1321ff.
Shooting method for difficult cases 753 1315f.
Shooting method interior fitting point 752 1315f. 1323ff.
Shuffling to improve random number generator 270 272
Side effects and PURE subprograms 960
Side effects prevented by data hiding 957 1209 1293 1296
Sidelobe fall-ff 548
Sidelobe level 548
sign() intrinsic function, modified in Fortran 95 961
Signal, bandwidth limited 495
Significance (numerical) 19
Significance (statistical) 609f.
Significance (statistical) one- vs. two-sided 632
Significance of 2-d K-S test 640 1281
Significance peak in Lomb periodogram 570
Significance two-tailed 613
SIMD machines (Single Instruction Multiple Data) 964 985f. 1009 1084f.
Similarity transform 452ff. 456 476 478 482
Simplex defined 402
Simplex method in linear programming 389 402 423ff. 431ff. 1216ff.
Simplex method of Nelder and Mead 389 402ff. 444 697f. 1208f. 1222ff.
Simplex recurrence 172
Simplex series 160
Simplex use in simulated annealing 444 1222ff.
Simpson’s rule 124ff. 128 133 136f. 583 782 788f. 1053f.
Simpson’s three-eighths rule 126 789f.
Simulated annealing see “Annealing method
Simulation see “Monte Carlo”
|
|
|
| Реклама |
|
|
|
|
|
О проекте