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