Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in FORTRAN77 :: Электронная библиотека попечительского совета мехмата МГУ

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Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in FORTRAN77

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Название: Numerical recipes in FORTRAN77

Авторы: Press W.H., Teukolsky S.A., Vetterling W.T.

Язык:

Рубрика: Математика/Численные методы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1992

Количество страниц: 973

Добавлена в каталог: 01.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

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 $K_{\nu}$       241
Series Bessel function $Y_{\nu}$       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”

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