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| Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in Fortran 90 |
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| Предметный указатель |
Fredholm equations 779f.
Fredholm equations, eigenvalue problems 780 785
Fredholm equations, error estimate in solution 784
Fredholm equations, first kind 779
Fredholm equations, Fredholm alternative 780
Fredholm equations, homogeneous vs. inhomogeneous 779f.
Fredholm equations, homogeneous, second kind 785 1325
Fredholm equations, ill-conditioned 780
Fredholm equations, infinite range 789
Fredholm equations, inverse problems 780 795ff.
Fredholm equations, kernel 779f.
Fredholm equations, nonlinear 781
Fredholm equations, Nystrom method 782ff. 789 1325
Fredholm equations, product Nystrom method 789 1328ff.
Fredholm equations, second kind 779f. 782ff. 1325 1331
Fredholm equations, subtraction of singularity 789
Fredholm equations, symmetric kernel 785 (see also Inverse problems)
Fredholm equations, with singularities 788 1328ff.
Fredholm equations, with singularities, worked example 792 1328ff.
Frequency domain 490
Frequency spectrum see Fast Fourier transform (FFT)
Frequentist, contrasted with Bayesian 810
Fresnel integrals 248ff.
Fresnel integrals, asymptotic form 249
Fresnel integrals, continued fraction 248f.
Fresnel integrals, routine for 249f. 1123
Fresnel integrals, series 248
Friday the Thirteenth 14f. 1011f.
FTCS (forward time centered space) 827ff. 839ff. 843
FTCS (forward time centered space), stability of 827ff. 839ff. 855
Full approximation storage (FAS) algorithm 874 1339ff.
Full moon 14f. 936 1011f.
Full multigrid method (FMG) 863 868 1334ff.
Full Newton methods, nonlinear least squares 683
Full pivoting 29 1014
Full weighting 867
Function, Airy 204 243f. 1121
Function, approximation 99ff. 184ff. 1043 1076ff.
Function, associated Legendre polynomial 246ff.. 764 1122f. 1319
Function, autocorrelation of 492
Function, bandwidth limited 495
Function, Bessel 172 204 223ff. 234 llOlff. 1115ff.
Function, Beta 209 1089
Function, binomial coefficients 208f. 1087f.
Function, branch cuts of 202f.
Function, chi-square probability 215 798
Function, complex 202
Function, confluent hypergeometric 204 239
Function, convolution of 492
Function, correlation of 492
Function, cosine integral 250f. 1123f.
Function, Coulomb wave 204 234
Function, cumulative binomial probability 222f.
Function, cumulative Poisson 209ff.
Function, Dawson’s integral 252ff. 600 1127f.
Function, digamma 216
Function, elliptic integrals 254ff. 906 1128ff.
Function, error 213f. 248 252 601 631 635 1094f. 1127 1276f.
Function, evaluation 159ff. 1070ff.
Function, evaluation by path integration 201f. 263 1138
Function, exponential integral 172 215ff. 250 1096f.
Function, F-distribution probability 222
Function, Fresnel integral 248ff. 1123
Function, Gamma 206 1085
Function, hypergeometric 202f. 263ff. 1138ff.
Function, incomplete beta 219ff. 610 1098ff. 1269
Function, incomplete gamma 209ff. 615 654 657f. 1089ff. 1272 1285
Function, inverse hyperbolic 178 255
Function, inverse trigonometric 255
Function, Jacobian elliptic 261 1137f.
Function, Kolmogorov — Smimov probability 618f. 640 1274 1281
Function, Legendre polynomial 172 246 674 1122 1291
Function, logarithm 255
Function, modified Bessel 229ff. 1109ff.
Function, modified Bessel, fractional order 239ff. 1118ff.
Function, overloading 1083
Function, parallel evaluation 986 1009 1084 1087 1090 1102 1128 1134
Function, path integration to evaluate 201f.
Function, pathological 99f. 343
Function, Poisson cumulant 214
Function, representations of 490
Function, routine for plotting a 342 1182
Function, sine and cosine integrals 248 250ff. 1125f.
Function, sn, dn, cn 261 1137f.
Function, spherical harmonics 246ff. 1122
Function, spheroidal harmonic 764ff. 770ff. 1319ff. 1323ff.
Function, Student’s probability 221f.
Function, variable number of arguments 1022
Function, Weber 204
Functional iteration, for implicit equations 740f.
FWHM (full width at half maximum) 548f.
Gamma deviate 282f. 1153f.
Gamma function 206ff. 1085
Gamma function, incomplete see Incomplete gamma function
Garbage collection 956
Gather-scatter operations 2/xiif. 984 1002 1032 1034
Gather-scatter operations, communication bottleneck 969 981 1250
Gather-scatter operations, many-to-one 984 1002 1032 1034
Gauss transformation 256
Gauss — Chebyshev integration 141 144 512f.
Gauss — Hermite integration 144 789
Gauss — Hermite integration, abscissas and weights 147 1062
Gauss — Hermite integration, normalization 147
Gauss — Jacobi integration 144
Gauss — Jacobi integration, abscissas and weights 148 1063
Gauss — Jordan elimination 27ff. 33 64 1014f.
Gauss — Jordan elimination, operation count 34 39
Gauss — Jordan elimination, solution of normal equations 667 1288
Gauss — Jordan elimination, storage requirements 30
Gauss — Kronrod quadrature 154
Gauss — Laguerre integration 144 789 1060
Gauss — Legendre integration 145f. 1059
Gauss — Lobatto quadrature 154 190 512
Gauss — Radau quadrature 154
Gauss — Seidel method (relaxation) 855 857 864ff. 1338
Gauss — Seidel method (relaxation), nonlinear 876 1341
Gaussian (normal) distribution 267 652 798
Gaussian (normal) distribution, central limit theorem 652f.
Gaussian (normal) distribution, deviates from 279f. 571 1152
Gaussian (normal) distribution, kurtosis of 606
Gaussian (normal) distribution, multivariate 690
Gaussian (normal) distribution, semi-invariants of 608
Gaussian (normal) distribution, tails compared to Poisson 653
Gaussian (normal) distribution, two-dimensional (binormal) 631
Gaussian (normal) distribution, variance of skewness of 606
Gaussian elimination 33f. 51 55 1014f.
Gaussian elimination, fill-in 45 64
Gaussian elimination, in reduction to Hessenberg form 478 1231
Gaussian elimination, integral equations 786 1326
Gaussian elimination, operation count 34
Gaussian elimination, outer product variant 1017
Gaussian elimination, relaxation solution of boundary value problems 753ff. 777 1316
Gaussian function, Hardy’s theorem on Fourier transforms 600 (see also Gaussian (normal) distribution)
Gaussian integration 127 140ff. 789 1059ff.
Gaussian integration, and orthogonal polynomials 142 1009 1061
Gaussian integration, calculation of abscissas and weights 142ff. 1009 1059ff.
Gaussian integration, error estimate in solution 784
Gaussian integration, extensions of 153f.
Gaussian integration, for integral equations 781 783 1325
Gaussian integration, from known recurrence relation 150 1064
Gaussian integration, Golub — Welsch algorithm for weights and abscissas 150 1064
Gaussian integration, nonclassical weight function 151f. 788f. 1064f. 1328f.
Gaussian integration, parallel calculation of formulas 1009 1061
Gaussian integration, preassigned nodes 153f.
Gaussian integration, weight function logic 153
Gaussian integration, weight functions 140ff. 788f. 1059ff. 1328f.
Gear’s method (stiff ODEs) 730
Geiger counter 266
Generalized eigenvalue problems 455
Generalized minimum residual method (GM — RES) 78
| Generic interface see Interface generic
Generic procedures 939 1083 1094 1096 1364
Generic procedures, elemental 940 942 946f. 1015 1083
Geometric progression 972 996f. 1365 1372ff.
geop() utility function 972 974 989 996 1127
Geophysics, use of Backus — Gilbert method 809
Gerchberg — Saxton algorithm 805
get_diag() utility function 985 989 1005 1226
Gilbert and Sullivan 714
Givens reduction 462f. 473
Givens reduction, fast 463
Givens reduction, operation count 463
Glassman, A.J. 180
Global optimization 387f. 436ff. 650 1219ff.
Global optimization, continuous variables 443f. 1222
Global variables 940 953f. 1210
Global variables, allocatable array method 954 1197 1212 1266 1287 1298
Global variables, communicated via internal subprogram 954 957f. 1067 1226
Global variables, danger of 957 1209 1293 1296
Global variables, pointer method 954 1197 1212 1266 1287 1302
Globally convergent minimization 418ff. 1215
Globally convergent root finding 373 376ff. 382 749f. 752 1196 1314f.
GMRES (generalized minimum residual method) 78
GNU Emacs 1/xvi
Godunov’s method 837
Golden mean (golden ratio) 21 349 392f. 399
Golden section search 341 389ff. 395 1202ff.
Golub — Welsch algorithm, for Gaussian quadrature 150 1064
Goodness-of-fit 650 654 657f. 662 690 1285
GOTO statements, danger of 9 959
Gram — Schmidt biorthogonalization 415f.
Gram — Schmidt orthogonalization 94 450f. 1039
Gram — Schmidt SVD as alternative to 58
Graphics, function plotting 342 1182f.
Gravitational potential 519
Gray code 300 881 886ff. 1344
Greenbaum, A. 79
Gregorian calendar 13 16 1011 1013
Grid square 116f.
Group, dihedral 894 1345
Guard digits 882 1343
Half weighting 867 1337
Halton’s quasi-random sequence 300
Hamming window 547
Hamming’s motto 341
Hann window 547
Harmonic analysis see Fourier transform
Hashing 293 1144 1148 1156
Hashing for random number seeds 1147f.
HDLC checksum 890
Heap (data structure) 327f. 336 897 1179
Heapsort 320 327f. 336 1171f. 1179
Helmholtz equation 852
Hermite polynomials 144 147
Hermite polynomials, approximation of roots 1062
Hermitian matrix 450ff. 475
Hertz (unit of frequency) 490
Hessenberg matrix 94 453 470 476ff. 488 1231
Hessian matrix 382 408 415f. 419f. 676ff. 803 815
Hessian matrix, is inverse of covariance matrix 667 679
Hessian matrix, second derivatives in 676
Hexadecimal constants 17f. 276 293
Hexadecimal constants, initialization 959
Hierarchically band diagonal matrix 598
Hierarchy of program structure 6ff.
High — Performance Fortran (HPF) 2/xvf. 964 981 984
High — Performance Fortran (HPF), scatter-with-add 1032
High-order not same as high-accuracy 100f. 124 389 399 705 709 741
High-pass filter 551
Hilbert matrix 83
Home page, Numerical Recipes 1/xx 2/xvii
Homogeneous linear equations 53
Hook step methods 386
Hotelling’s method for matrix inverse 49 598
Householder transformation 52 453 462ff. 469 473 475 478 481f. 1227f.
Householder transformation, in QR decomposition 92 1039
Householder transformation, operation count 467
HPF see High — Performance Fortran
HR (infinite impulse response) filter 552ff. 566
Huffman coding 564 881 896f. 902 1346ff.
huge() intrinsic function 951
Hyperbolic functions, explicit formulas for inverse 178
Hyperbolic partial differential equations 818
Hyperbolic partial differential equations, advective equation 826
Hyperbolic partial differential equations, flux-conservative initial value problems 825ff.
Hypergeometric function 202f. 263ff.
Hypergeometric function, routine for 264f. 1138
Hypothesis, null 603
I2B, defined 937
I4B, defined 937
iand() intrinsic function 951
ibclr()intrinsic function 951
ibits() intrinsic function 951
IBM 1/xxiii 2/xix
IBM checksum 894
IBM, bad random number generator 268
IBM, Fortran 90 compiler 2/viii
IBM, PC 4 276 293 886
IBM, PC — RT 4
IBM, radix base for floating point arithmetic 476
IBM, RS6000 2/viii 4
ibset() intrinsic function 951
ICCG (incomplete Cholesky conjugate gradient method) 824
ICF (intrinsic correlation function) model 817
Identity (unit) matrix 25
IEEE floating point format 276 882f. 1343
ieor()intrinsic function 951
if statement, arithmetic 2/xi
if structure 12f.
ifirstloc() utility function 989 993 1041 1346
Ill-conditioned integral equations 780
Image processing 519 803
Image processing, as an inverse problem 803
Image processing, cosine transform 513
Image processing, fast Fourier transform (FFT) 519 523 803
Image processing, from modulus of Fourier transform 805
Image processing, maximum entropy method (MEM) 809ff.
Image processing, wavelet transform 596f. 1267f.
imaxloc() utility function 989 993 1017
iminloc() utility function 989 993 1046 1076
Implicit differencing 827
Implicit differencingfor diffusion equation 840
Implicit differencingfor stiff equations 729 740 1308
Implicit function theorem 340
IMPLICIT NONE statement 2/xiv 936
Implicit pivoting 30 1014
Implicit shifts in QL method 472ff.
Implied do-list 968 971 1127
Importance sampling, in Monte Carlo 306f.
Improper integrals 135ff. 1055
Impulse response function 531 540 552
IMSL 1/xxiii 2/xx 26 64 205 364 369 454
In-place selection 335 1178f.
Included file, superseded by module 940
incomplete see Incomplete beta function
Incomplete beta function 219ff. 1098ff.
Incomplete beta function for F-test 613
Incomplete beta function for Student’s t 610 613 1269
Incomplete beta function, routine for 220f. 1097
Incomplete Cholesky conjugate gradient method (ICCG) 824
Incomplete gamma function 209ff. 1089ff.
Incomplete gamma function, deviates from 282f. 1153
Incomplete gamma function, for chi-square 615 654 657f. 1272 1285
Incomplete gamma function, in mode estimation 610
Incomplete gamma function, routine for 211f. 1089
Increment of linear congruential generator 268
Indentation of blocks 9
INDEX 934ff. 1446ff.
Index loss 967f. 1038
Index table 320 329f. 1173ff. 1176
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