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| Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in Fortran 90 |
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| Предметный указатель |
Index this entry 1464
Inequality constraints 423
inheritance 8
Initial value problems 702 818f.
Initialization expression 943 959 1012 1127
Initialization of derived data type 2/xv
Injection operator 864 1337
Instability see Stability
Integer model, in Fortran 90 1144 1149 1156
Integer programming 436
Integra-differential equations 782
Integral equations 779ff.
Integral equations, adaptive stepsize control 788
Integral equations, block-by-block method 788
Integral equations, correspondence with linear algebraic equations 779ff.
Integral equations, degenerate kernel 785
Integral equations, eigenvalue problems 780 785
Integral equations, error estimate in solution 784
Integral equations, Fredholm 779f. 782ff. 1325 1331
Integral equations, Fredholm alternative 780
Integral equations, homogeneous, second kind 785 1325
Integral equations, ill-conditioned 780
Integral equations, infinite range 789
Integral equations, inverse problems 780 795ff.
Integral equations, kernel 779
Integral equations, nonlinear 781 787
Integral equations, Nystrom method 782ff. 789 1325
Integral equations, product Nystrom method 789 1328ff.
Integral equations, subtraction of singularity 789
Integral equations, symmetric kernel 785
Integral equations, unstable quadrature 787f.
Integral equations, Volterra 780f. 786ff. 1326f.
Integral equations, wavelets 782 (see also Inverse problems)
Integral equations, with singularities 788ff. 1328ff.
Integral equations, with singularities, worked example 792 1328ff.
Integral operator, wavelet approximation of 597 782
Integration of functions 123ff. 1052ff.
Integration of functions, cosine integrals 250 1125
Integration of functions, Fourier integrals 577ff. 1261
Integration of functions, Fourier integrals, infinite range 583
Integration of functions, Fresnel integrals 248 1123
Integration of functions, Gauss — Hermite 147f. 1062
Integration of functions, Gauss — Jacobi 148 1063
Integration of functions, Gauss — Laguerre 146 1060
Integration of functions, Gauss — Legendre 145 1059
Integration of functions, integrals that are elliptic integrals 254
Integration of functions, path integration 201f.
Integration of functions, sine integrals 250 1125
INTENT attribute 1072 1092
Interface (Fortran 90) 939 942 1067
Interface (Fortran 90), explicit 939 942 1067 1384
Interface (Fortran 90), for communication between program parts 957 1209 1293 1296
Interface (Fortran 90), for Numerical Recipes 1384ff.
Interface (Fortran 90), generic 2/xiii 940 1015 1083 1094 1096
Interface (Fortran 90), implicit 939
Interface block 939 1084 1384
Interface, in programs 2 8
Intermediate Value Theorem 343
Internal subprogram (Fortran 90) 2/xiv 954 957 1067 1202f. 1226
Internal subprogram (Fortran 90), nesting of 2/xii
Internal subprogram (Fortran 90), resembles C macro 1302
Internal subprogram (Fortran 90), supersedes statement function 1057 1256
International Standards Organization (ISO) 2/xf. 2/xiii
Internet, availability of code over 1/xx 2/xvii
Interpolation 99ff.
Interpolation, Aitken’s algorithm 102
Interpolation, and ordinary differential equations 101
Interpolation, avoid 2-stage method 100
Interpolation, avoid in Fourier analysis 569
Interpolation, bicubic 118f. 1049f.
Interpolation, bilinear 117
Interpolation, caution on high-order 100
Interpolation, coefficients of polynomial 100 113ff. 191 575 1047f. 1078
Interpolation, error estimates for 100
Interpolation, for computing Fourier integrals 578
Interpolation, in multigrid method 866 1337
Interpolation, inverse quadratic 353 395ff. 1204
Interpolation, multidimensional 101f. 116ff. 1049ff.
Interpolation, Neville’s algorithm 102f. 182 1043
Interpolation, Nystrom 783 1326
Interpolation, of functions with poles 104ff. 1043f.
Interpolation, offset arrays 104
Interpolation, operation count for 100
Interpolation, operator 864 1337
Interpolation, order of 100
Interpolation, oscillations of polynomial 100 116 389 399
Interpolation, parabolic, for minimum finding 395 1204
Interpolation, polynomial 99 102ff. 182 1043
Interpolation, rational Chebyshev approximation 197ff. 1081
Interpolation, rational function 99 104ff. 194ff. 225 718ff. 726 1043f. 1080 1306
Interpolation, reverse (extirpolation) 574 1261
Interpolation, spline 100 107ff. 120f. 1044f. 1050f.
Interpolation, trigonometric 99 (see also Fitting)
Interprocessor communication 969 981
Interval variable (statistics) 623
Intrinsic correlation function (ICF) model 817
Intrinsic data types 937
Intrinsic procedures, array inquiry 938 942 948ff.
Intrinsic procedures, array manipulation 950
Intrinsic procedures, array reduction 948
Intrinsic procedures, array unary and binary functions 949
Intrinsic procedures, backwards-compatibility 946
Intrinsic procedures, bit manipulation 2/xiii 951
Intrinsic procedures, character 952
Intrinsic procedures, cmplx 1254
Intrinsic procedures, conversion elemental 946
Intrinsic procedures, elemental 940 942 946f. 951 1083 1364
Intrinsic procedures, generic 939 1083f. 1364
Intrinsic procedures, lexical comparison 952
Intrinsic procedures, numeric inquiry 2/xiv 1107 1231 1343
Intrinsic procedures, numerical 946 951f.
Intrinsic procedures, numerical representation 951
Intrinsic procedures, pack used for sorting 1171
Intrinsic procedures, random_number 1143
Intrinsic procedures, real 1254
Intrinsic procedures, top 10 945
Intrinsic procedures, truncation 946f. (see also Fortran 90)
Inverse hyperbolic function 178 255
Inverse iteration see Eigensystems
Inverse problems 779 795ff.
Inverse problems, and integral equations 780
Inverse problems, Backus — Gilbert method 806ff.
Inverse problems, Bayesian approach 799 810f. 816f.
Inverse problems, central idea 799
Inverse problems, constrained linear inversion method 799ff.
Inverse problems, data inversion 807
Inverse problems, deterministic constraints 804ff.
Inverse problems, Gerchberg — Saxton algorithm 805
Inverse problems, in geophysics 809
Inverse problems, incomplete Fourier coefficients 813
Inverse problems, linear regularization 799ff.
Inverse problems, maximum entropy method (MEM) 810 815f.
Inverse problems, MEM demystified 814
Inverse problems, Phillips — Twomey method 799ff.
Inverse problems, principal solution 797
Inverse problems, regularization 796ff.
Inverse problems, regularizing operator 798
Inverse problems, stabilizing functional 798
Inverse problems, Tikhonov — Miller regularization 799ff.
Inverse problems, trade-off curve 795
Inverse problems, trade-off curve, Backus — Gilbert method 809
Inverse problems, two-dimensional regularization 803
Inverse problems, use of conjugate gradient minimization 804 815
Inverse problems, use of convex sets 804
Inverse problems, use of Fourier transform 803 805
Inverse problems, Van Cittert’s method 804
Inverse quadratic interpolation 353 395ff. 1204
Inverse response kernel, in Backus — Gilbert method 807
Inverse trigonometric function 255
ior() intrinsic function 951
| ISBN (International Standard Book Number) checksum 894
ishft() intrinsic function 951
ishftc() intrinsic function 951
ISO (International Standards Organization) 2/xf. 2/xiii
Iterated integrals 155
Iteration 9f.
Iteration matrix 856
Iteration, for linear algebraic equations 26
Iteration, functional 740f.
Iteration, in root finding 340f.
Iteration, required for two-point boundary value problems 745
Iteration, to improve solution of linear algebraic equations 47ff. 195 1022
ITPACK 71
Iverson, John 2/xi
Jacobi matrix, for Gaussian quadrature 150 1064
Jacobi polynomials, approximation of roots 1064
Jacobi transformation (or rotation) 94 453 456ff. 462 475 489 1041 1225
Jacobian determinant 279 774
Jacobian elliptic functions 261 1137f.
Jacobian matrix 374 376 379 382 731 1197f. 1309
Jacobian matrix, singular in Newton’s rule 386
Jacobi’s method (relaxation) 855ff. 864
Jenkins — Traub method 369
Julian Day 1 13 16 936 1010ff.
Jump transposition errors 895
K-S test see Kolmogorov — Smimov test
Kalman filter 700
Kanji 2/xii
Kaps — Rentrop method 730 1308
Kendall’s tau 634 637ff. 1279
Kennedy, Ken 2/xv
Kepler’s equation 1061
Kermit checksum 889
Kernel 779
Kernel, averaging, in Backus — Gilbert method 807
Kernel, degenerate 785
Kernel, finite rank 785
Kernel, inverse response 807
Kernel, separable 785
Kernel, singular 788f. 1328
kernel, symmetric 785
Keys used in sorting 329 889
Keyword argument 2/xiv 947f. 1341
KIND parameter 946 1261 1284
KIND parameter, and cmplx() intrinsic function 1125 1192 1254
KIND parameter, and real() intrinsic function 1125
KIND parameter, default 937
KIND parameter, for Numerical Recipes 1361
KIND parameter, for random numbers 1144
kind() intrinsic function 951
Kolmogorov — Smimov test 614 617ff. 694 1273f.
Kolmogorov — Smimov test, two-dimensional 640 1281f.
Kolmogorov — Smimov test, variants 620ff. 640 1281
Kuiper’s statistic 621
kurtosis 606 608 1269
L-estimate 694
l0f.
Labels, statement 9
Lag 492
Lagged Fibonacci generator 1142 1148ff.
Lagrange multiplier 795
Lagrange’s formula for polynomial interpolation 84 102f. 575 578
Laguerre polynomials, approximation of roots 1061
Laguerre’s method 341 365f. 1191f.
Lanczos lemma 498f.
Lanczos method for gamma function 206 1085
Landen transformation 256
LAPACK 26 1230
Laplace’s equation 246 818
Las Vegas 625
Latin square or hypercube 305f.
Laurent series 566
Lax method 828ff. 836 845f.
Lax method, multidimensional 845f.
Lax — Wendroff method 835ff.
lbound() intrinsic function 949
Leakage in power spectrum estimation 544 548
Leakage width 548f.
Leapfrog method 833f.
Least squares filters see Savitzky — Golay filters
Least squares fitting 645 651f. 655ff. 660ff. 665ff. 1285f. 1288f.
Least squares fitting, as M-estimate for normal errors 696
Least squares fitting, as maximum likelihood estimator 652
Least squares fitting, as method for smoothing data 645 1283
Least squares fitting, contrasted to general minimization problems 684ff.
Least squares fitting, degeneracies in 671f. 674
Least squares fitting, for rational Chebyshev approximation 199f. 1081f.
Least squares fitting, for spectral analysis 570 1258
Least squares fitting, Fourier components 570 1258
Least squares fitting, freezing parameters in 668 700
Least squares fitting, general linear case 665ff. 1288 1290f.
Least squares fitting, Levenberg — Marquardt method 678ff. 816 1292f.
Least squares fitting, Lomb periodogram 570 1258
Least squares fitting, multidimensional 675
Least squares fitting, nonlinear 386 675ff. 816 1292
Least squares fitting, nonlinear, advanced methods 683
Least squares fitting, normal equations 645 666f. 800 1288
Least squares fitting, normal equations often singular 670 674
Least squares fitting, optimal (Wiener) filtering 540f.
Least squares fitting, QR method in 94 668
Least squares fitting, relation to linear correlation 630 658
Least squares fitting, Savitzky — Golay filter as 645 1283
Least squares fitting, singular value decomposition (SVD) 25f. 51f. 199f. 670ff. 1081 1290
Least squares fitting, skewed by outliers 653
Least squares fitting, standard (probable) errors on fitted parameters 667 671 1288 1290
Least squares fitting, weighted 652 1285
Left eigenvalues or eigenvectors 451
Legal matters 1/xx 2/xvii
Legendre elliptic integral see Elliptic integrals
Legendre polynomials 246 1122
Legendre polynomials, fitting data to 674 1291f.
Legendre polynomials, recurrence relation 172
Legendre polynomials, shifted monic 151 (see also Associated Legendre polynomials; Spherical harmonics)
Lehmer — Schur algorithm 369
Lemarie’s wavelet 593
Lentz’s method for continued fraction 165 212
Lepage, P. 309
Leptokurtic distribution 606
Levenberg — Marquardt algorithm 386 678ff. 816 1292
Levenberg — Marquardt algorithm, advanced implementation 683
Levinson’s method 86 1038
Lewis, H.W. 275
Lexical comparison functions 952
LGT, defined 937
License information 1/xx 2/xviiff.
Limbo 356
Limit cycle, in Laguerre’s method 365
Line minimization see Minimization along
Line search see Minimization along
Linear algebra, intrinsic functions for parallelization 969f. 1026 1040 1200 1326
Linear algebraic equations 22ff. 1014
Linear algebraic equations, and integral equations 779ff. 783 1325
Linear algebraic equations, band diagonal 43ff. 1019
Linear algebraic equations, biconjugate gradient method 77 1034ff.
Linear algebraic equations, Cholesky decomposition 89f. 423 455 668 1038f.
Linear algebraic equations, complex 41
Linear algebraic equations, computing  40
Linear algebraic equations, conjugate gradient method 77ff. 599 1034
Linear algebraic equations, cyclic tridiagonal 67 1030
Linear algebraic equations, direct methods 26 64 1014 1030
Linear algebraic equations, Fortran 90 vs. library routines 1016
Linear algebraic equations, Gauss — Jordan elimination 27ff. 1014
Linear algebraic equations, Gaussian elimination 33f. 1014f.
Linear algebraic equations, Hilbert matrix 83
Linear algebraic equations, Hotelling’s method 49 598
Linear algebraic equations, iterative improvement 47ff. 195 1022
Linear algebraic equations, iterative methods 26 77ff. 1034
Linear algebraic equations, large sets of 23
Linear algebraic equations, least squares solution 53ff. 57f. 199f. 671 1081 1290
Linear algebraic equations, LU decomposition 34ff. 195 386 732 783 786 801 1016 1022 1325f.
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