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

Polynomial interpolation smoothing filters      645 (see also “Interpolation”)
Polynomials      167ff.
Polynomials algebraic manipulations      169 1072
Polynomials approximate roots of Hermite polynomials      1062
Polynomials approximate roots of Jacobi polynomials      1064
Polynomials approximate roots of Laguerre polynomials      1061
Polynomials approximating modified Bessel functions      230
Polynomials approximation from Chebyshev coefficients      191 1078f.
Polynomials AUTODIN-II      890
Polynomials CCITT      889f.
Polynomials characteristic      368 1193
Polynomials characteristic, for digital filters      554 559 1257
Polynomials characteristic, for eigenvalues of matrix      449 469
Polynomials Chebyshev      184ff. 1076ff.
Polynomials coefficients from roots      980
Polynomials CRC-16      890
Polynomials cumulants of      977 999 1071f. 1192 1365 1378f.
Polynomials deflation      362ff. 370f. 977
Polynomials derivatives of      167 978 1071
Polynomials division      84 169 362 370 977 1072
Polynomials evaluation of      167 972 977 998f. 1071 1258 1365 1376ff.
Polynomials evaluation of derivatives      167 978 1071
Polynomials extrapolation in Bulirsch — Stoer method      724 726 1305f.
Polynomials extrapolation in Romberg integration      134
Polynomials fitting      83 114 191 645 665 674 1078f. 1291
Polynomials generator for CRC      889
Polynomials ill-conditioned      362
Polynomials masked evaluation of      1378
Polynomials matrix method for roots      368 1193
Polynomials minimax      186 198 1076
Polynomials monic      142f.
Polynomials multiplication      169
Polynomials operation count for      168
Polynomials orthonormal      142 184 1009 1061
Polynomials parallel operations on      977ff. 998f. 1071f. 1192
Polynomials primitive modulo      2 287ff. 301f. 889
Polynomials roots of      178ff. 362ff. 368 1191ff.
Polynomials shifting of      192f. 978 1079
Polynomials stopping criterion in root finding      366
poly_term() utility function      974 977 989 999 1071f. 1192
Port, serial data      892
Portability      3 963
Portable random number generator      see “Ran — Random number generator”
Positive definite matrix, testing for      90
Positivity constraints      423
Postal Service (U.S.), barcode      894
PostScript      1/xvi 1/xxiii 2/xx
Powell’s method      389 402 406ff. 1210ff.
Power (in a signal)      492f.
Power series      159ff. 167 195
Power series economization of      192f. 1061 1080
Power spectral density      see “Fourier transform”; “Spectral density”
Power spectrum estimation      see “Fourier transform”; “Spectral density”
PowerStation, Microsoft Fortran      2/xix
PPM (piecewise parabolic method)      837
Precision converting to double      1362
Precision floating point      882 937 1343 1361ff.
Precision multiple      906ff. 1352ff. 1362
Preconditioned biconjugate gradient method (PBCG)      78f.
Preconditioning, in conjugate gradient methods      824
Predictor-corrector methods      702 730 740ff.
Predictor-corrector methods Adams — Bashforth — Moulton schemes      741
Predictor-corrector methods adaptive order methods      744
Predictor-corrector methods compared to other methods      740
Predictor-corrector methods fallacy of multiple correction      741
Predictor-corrector methods functional iteration vs. Newton’s rule      742
Predictor-corrector methods multivalue compared with multistep      742ff.
Predictor-corrector methods present() intrinsic function      952
Predictor-corrector methods starting and stopping      742 744
Predictor-corrector methods stepsize control      742f.
Predictor-corrector methods with fixed number of iterations      741
Prime numbers      915
Primitive polynomials modulo 2      287ff. 301f. 889
Principal directions      408f. 1210
Principal solution, of inverse problem      797
PRIVATE attribute      957 1067
Prize, $1000offered      272 1141 1150f.
probability      see “Random number generator”; “Statistical tests”
Probability density, change of variables in      278f.
Procedure      see “Program(s)”; “Subprogram”
Process loss      548
Product Nystrom method      789 1331
product() intrinsic function      948
Program as black boxes      1/xviii 6 26 52 205 341 406
Program encapsulation      7
Program modularization      7f.
Program organization      5ff.
Program typography of      2f. 12 937
Program validation      3f.
Programming, serial vs. parallel      965 987
Programs dependencies      921ff. 1434ff.
Programs interfaces      2 8
Programs type declarations      2
Projection onto convex sets (POCS)      805
Projection operator, nonexpansive      805
Prolongation operator      864 1337
Protocol, for communications      888
PSD (power spectral density)      see “Fourier transform”; “Spectral density”
Pseudo-random numbers      266ff. 1141ff.
PUBLIC attribute      957 1067
Puns, particularly bad      167 744 747
PURE attribute      2/xv 960f. 964 986
put_diag() utility function      985 990 1005 1200
Pyramidal algorithm      586 1264
Pythagoreans      392
QL      see “Eigensystems”
qr      see “Eigensystems”
QR decomposition      91f. 382 386 1039f. 1199
QR decomposition and least squares      668
QR decomposition backsubstitution      92 1040
QR decomposition operation count      92
QR decomposition pivoting      92
QR decomposition updating      94 382 386 1041 1199
QR decomposition use for orthonormal basis      58 94
Quadratic convergence      49 256 351 356 409f. 419 906
Quadratic equations      20 178 391 457
Quadratic interpolation      353 364
Quadratic programming      436
Quadrature      123ff. 1052ff.
Quadrature adaptive      123 190 788
Quadrature alternative extended Simpson’s rule      128
Quadrature and computer science      881
Quadrature arbitrary weight function      151ff. 789 1064 1328
Quadrature automatic      154
Quadrature Bode’s rule      126
Quadrature by Chebyshev fitting      124 189 1078
Quadrature by cubic splines      124
Quadrature change of variable in      137ff. 788 1056ff.
Quadrature classical formulas for      124ff.
Quadrature Clenshaw — Curtis      124 190 512f.
Quadrature closed formulas      125 127f.
Quadrature error estimate in solution      784
Quadrature extended midpoint rule      129f. 135 1054f.
Quadrature extended rules      127ff. 134f. 786 788ff. 1326 1328
Quadrature extended Simpson’s rule      128
Quadrature for improper integrals      135ff. 789 1055 1328
Quadrature for integral equations      781f. 786 1325ff.
Quadrature Fourier integrals      577ff. 1261ff.
Quadrature Fourier integrals, infinite range      583
Quadrature Gauss — Chebyshev      144 512f.
Quadrature Gauss — Hermite      144 789 1062
Quadrature Gauss — Jacobi      144 1063
Quadrature Gauss — Kronrod      154
Quadrature Gauss — Laguerre      144 789 1060
Quadrature Gauss — Legendre      144 783 789 1059 1325
Quadrature Gauss — Lobatto      154 190 512
Quadrature Gauss — Radau      154
Quadrature Gaussian integration      127 140ff. 781 783 788f. 1009 1059ff. 1325 1328f.
Quadrature Gaussian integration, nonclassical weight function      151ff. 788f. 1064f. 1328f.
Quadrature mirror filter      585 593

Quadrature Monte Carlo      124 155ff. 295ff. 306ff. 1161ff.
Quadrature multidimensional      124 155ff. 1052 1065ff.
Quadrature multidimensional, by recursion      1052 1065
Quadrature Newton — Cotes formulas      125ff. 140
Quadrature open formulas      125ff. 129f. 135
Quadrature related to differential equations      123
Quadrature related to predictor — corrector methods      740
Quadrature Romberg integration      124 134f. 137 182 717 788 1054f. 1065 1067
Quadrature semi-open formulas      130
Quadrature Simpson’s rule      126 133 136f. 583 782 788ff. 1053
Quadrature Simpson’s three-eighths rule      126 789f.
Quadrature singularity removal      137ff. 788 1057ff. 1328ff.
Quadrature singularity removal, worked example      792 1328ff.
Quadrature trapezoidal rule      125 127 130ff. 134f. 579 583 782 786 1052ff. 1326f.
Quadrature using FFTs      124
Quadrature weight function logx      153 (see also “Integration of functions”)
Quantum mechanics, Uncertainty Principle      600
Quartile value      320
Quasi — Newton methods for minimization      390 418ff. 1215
Quasi-andom sequence      299ff. 318 881 888
Quasi-andom sequence for Monte Carlo integration      304 309 318
Quasi-andom sequence Halton’s      300
Quasi-andom sequence Sobol’s      300ff. 1160
Quicksort      320 323ff. 330 333 1169f.
Quotient-difference algorithm      164
R-estimates      694
Radioactive decay      278
Radix base for floating point arithmetic      476 882 907 913 1231 1343 1357
Radix conversion      902 906 913 1357
Radix sort      1172
radix() intrinsic function      1231
Ramanujan’s identity for n      915
Random bits, generation of      287ff. 1159f.
Random deviates      266ff. 1141ff.
Random deviates binomial      285f. 1155
Random deviates exponential      278 1151f.
Random deviates gamma distribution      282f. 1153
Random deviates Gaussian      267 279f. 571 798 1152f.
Random deviates normal      267 279f. 571 1152f.
Random deviates Poisson      283ff. 571 1154f.
Random deviates quasi-random sequences      299ff. 881 888 1160f.
Random deviates uniform      267ff. 1158f. 1166
Random deviates uniform integer      270 274ff.
Random number generator      266ff. 1141ff.
Random number generator bitwise operations      287
Random number generator Box — Muller algorithm      279 1152
Random number generator Data Encryption Standard      290ff. 1144 1156ff.
Random number generator for integer — valued probability distribution      283f. 1154
Random number generator good choices for modulus, multiplier and increment      274ff.
Random number generator in Quicksort      324
Random number generator in simulated annealing method      438
Random number generator initializing      1144ff.
Random number generator integer vs. real implementation      273
Random number generator lagged Fibonacci generator      1142 1148ff.
Random number generator linear congruential generator      267ff. 1142
Random number generator L’Ecuyer’s long period      271f.
Random number generator machine language      269
Random number generator Marsaglia shift register      1142 1148ff.
Random number generator Minimal Standard, Park and Miller’s      269 1142
Random number generator nonrandomness of low-order bits      268f.
Random number generator parallel      1009
Random number generator perfect      272 1141 1150f.
Random number generator planes, numbers lie on      268
Random number generator portable      269ff. 1142
Random number generator primitive polynomials modulo 2      287ff.
Random number generator pseudo-DES      291 1144 1156ff.
Random number generator quasi-random sequences      299ff. 881 888 1160f.
Random number generator quick and dirty      274
Random number generator quicker and dirtier      275
Random number generator random access to nth number      293
Random number generator random bits      287ff. 1159f.
Random number generator recommendations      276f.
Random number generator rejection method      281ff.
Random number generator serial      1141f.
Random number generator shuffling procedure      270 272
Random number generator spectral test      274
Random number generator state space      1143f.
Random number generator state space exhaustion      1141
Random number generator subtractive method      273 1143
Random number generator system-supplied      267f.
Random number generator timings      276f. 1151
Random number generator transformation method      277ff.
Random number generator trick for trigonometric functions      280
Random numbers      see “Monte Carlo”; “Random deviates”
Random walk      20
random_number() intrinsic function      1141 1143
random_seed() intrinsic function      1141
RANDU, infamous routine      268
RANGE      53f.
Rank (matrix)      53
Rank (matrix) kernel of finite      785
Rank (sorting)      320 332 1176
Rank (statistics)      633ff. 694f. 1277
Rank (statistics) Kendall’s tau      637ff. 1279
Rank (statistics) Spearman correlation coefficient      634f. 1277ff.
Rank (statistics) sum squared differences of      634 1277
Ratio variable (statistics)      623
Rational Chebyshev approximation      197ff. 1081f.
Rational function      99 167ff. 194ff. 1080f.
Rational function approximation for Bessel functions      225
Rational function approximation for continued fraction      164 211 219f.
Rational function as power spectrum estimate      566
Rational function as power spectrum estimate interpolation and extrapolation using      1043f. 1080ff. 1306
Rational function Chebyshev approximation      197ff. 1081f.
Rational function evaluation of      170 1072f.
Rational function extrapolation in Bulirsch — Stoer method      718ff. 726 1306f.
Rational function interpolation and extrapolation using      99 104ff. 194ff. 718ff. 726
Rational function minimax      198
Re-entrant procedure      1052
real() intrinsic function, ambiguity of      947
Realizable (causal)      552 554f.
reallocate() utility function      955 990 992 1070 1302
Rearranging      see “Sorting”
Reciprocal, multiple precision      910f. 1355f.
Record, in data file      329
Recurrence relation      172ff. 971ff.
Recurrence relation, and continued fraction      175
Recurrence relation, arithmetic progression      971f. 996
Recurrence relation, associated Legendre polynomials      247
Recurrence relation, Bessel function      172 224 227f. 234
Recurrence relation, binomial coefficients      209
Recurrence relation, Bulirsch — Stoer      105f.
Recurrence relation, characteristic polynomial of tridiagonal matrix      469
Recurrence relation, Clenshaw’s recurrence formula      176f.
Recurrence relation, continued fraction evaluation      164f.
Recurrence relation, convergence      175
Recurrence relation, cosine function      172 500
Recurrence relation, cyclic reduction      974
Recurrence relation, dominant solution      174
Recurrence relation, exponential integrals      172
Recurrence relation, for polynomial cumulants      977 999 1071f.
Recurrence relation, gamma function      206
Recurrence relation, generation of random bits      287f.
Recurrence relation, geometric progression      972 996
Recurrence relation, Golden Mean      21
Recurrence relation, Legendre polynomials      172
Recurrence relation, minimal vs. dominant solution      174
Recurrence relation, modified Bessel function      232
Recurrence relation, Neville’s      103 182
Recurrence relation, orthonormal polynomials      142
Recurrence relation, Perron’s theorems      174f.
Recurrence relation, Pincherle’s theorem      175
Recurrence relation, polynomial interpolation      103 183
Recurrence relation, primitive polynomials modulo      2 287f.
Recurrence relation, random number generator      268
Recurrence relation, rational function interpolation      105f. 1043
Recurrence relation, recursive doubling      973 977 988 999 1071f. 1073
Recurrence relation, second order      974f. 1074
Recurrence relation, sequence of trig functions      173
Recurrence relation, sine function      172 500

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