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| Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in Fortran 90 |
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| Предметный указатель |
Minimization, Davidon — Fletcher — Powell algorithm 390 418ff. 1215
Minimization, degenerate 795
Minimization, direction-set methods 389 406ff. 1210ff.
Minimization, downhill simplex method 389 402ff. 444 697f. 1208 1222ff.
Minimization, finding best-fit parameters 650
Minimization, Fletcher — Reeves algorithm 390 414ff. 1214
Minimization, functional 795
Minimization, global 387f. 443f. 650 1219 1222
Minimization, globally convergent multidimensional 418 1215
Minimization, golden section search 390ff. 395 1202ff.
Minimization, in nonlinear model fitting 675f. 1292
Minimization, multidimensional 388f. 402ff. 1208ff. 1214
Minimization, Polak — Ribiere algorithm 389 414ff. 1214
Minimization, Powell’s method 389 402 406ff. 1210ff.
Minimization, quasi-Newton methods 376 390 418ff. 1215
Minimization, scaling of variables 420
Minimization, steepest descent method 414 804
Minimization, termination criterion 392 404
Minimization, use for sparse linear systems 77ff.
Minimization, use in finding double roots 341
Minimization, using derivatives 389f. 399ff. 1205ff.
Minimization, variable metric methods 390 418ff. 1215
Minimum residual method, for sparse system 78
minloc() intrinsic function 949 992f.
minloc() intrinsic function, modified in Fortran 95 961
MINPACK 683
minval() intrinsic function 948 961
mips 886
Missing data problem 569
Mississippi River 438f. 447
MMP (massively multiprocessor) machines 965ff. 974 981 984 1016ff. 1021 1045 1226ff. 1250
Mode of distribution 605 609
Model-trust region 386 683
Modeling of data see Fitting
Modes, homogeneous, of recursive filters 554
Modified Bessel functions see Bessel functions
Modified Lentz’s method, for continued fractions 165
Modified midpoint method 716ff. 720 1302f.
Modified moments 152
Modula-2 7
Modular arithmetic, without overflow 269 271 275
Modular programming 2/xiii 7f. 956ff. 1209 1293 1296 1346
MODULE facility 2/xiii 936f. 939f. 957 1067 1298 1320 1322 1324 1330 1346
MODULE facility, in nr.f90 936 941f. 1362 1384ff.
MODULE facility, in nrtype.f90 936f. 1361f.
MODULE facility, in nrutil.f90 936 1070 1362 1364ff.
MODULE facility, initializing random number generator 1144ff.
MODULE facility, sparse matrix 1031
MODULE facility, undefined variables on exit 953 1266
Module subprogram 940
modulo() intrinsic function 946 1156
Modulus of linear congruential generator 268
Moments, and quadrature formulas 791 1328
Moments, filter that preserves 645
Moments, modified problem of 151f.
Moments, of distribution 604ff. 1269
Moments, problem of 83
Moments, semi-invariants 608
Monic polynomial 142f.
Monotonicity constraint, in upwind differencing 837
Monte Carlo 155ff. 267
Monte Carlo, adaptive 306ff. 1161ff.
Monte Carlo, and Kolmogorov — Smimov statistic 622 640
Monte Carlo, bootstrap method 686f.
Monte Carlo, comparison of sampling methods 309
Monte Carlo, exploration of binary tree 290
Monte Carlo, importance sampling 306f.
Monte Carlo, integration 124 155ff. 295ff. 306ff. 1161
Monte Carlo, integration, recursive 314ff. 1164ff.
Monte Carlo, integration, using Sobol’ sequence 304
Monte Carlo, integration, VEGAS algorithm 309ff. 1161
Monte Carlo, partial differential equations 824
Monte Carlo, quasi-random sequences in 299ff.
Monte Carlo, quick and dirty 686f.
Monte Carlo, recursive 306ff. 314ff. 1161 1164ff.
Monte Carlo, significance of Lomb periodogram 570
Monte Carlo, simulation of data 654 684ff. 690
Monte Carlo, stratified sampling 308f. 314 1164
Moon, calculate phases of 1f. 14f. 936 1010f.
Mother functions 584
Mother Nature 684 686
Moving average (MA) model 566
Moving window averaging 644
Mozart 9
ms 1/xxii 2/xix
Muller’s method 364 372
Multidimensional confidence levels of fitting 688f.
Multidimensional data, use of binning 623
Multidimensional Fourier transform 515ff. 1241 1246 1251
Multidimensional Fourier transform, real data 519ff. 1248f.
Multidimensional initial value problems 844ff.
Multidimensional integrals 124 155ff. 295ff. 306ff. 1065ff. 1161ff.
Multidimensional interpolation 116ff. 1049ff.
Multidimensional Kolmogorov — Smimov test 640 1281
Multidimensional least squares fitting 675
Multidimensional minimization 402ff. 406ff. 413ff. 1208ff. 1214f. 1222ff.
Multidimensional Monte Carlo integration 295ff. 306ff. 1161ff.
Multidimensional normal (Gaussian) distribution 690
Multidimensional optimization 388f.
Multidimensional partial differential equations 844ff.
Multidimensional root finding 340ff. 358 370 372ff. 746 749f. 752 754 1194ff. 1314ff.
Multidimensional search using quasi-random sequence 300
Multidimensional secant method 373 382f. 1199f.
Multidimensional wavelet transform 595 1267f.
Multigrid method 824 862ff. 1334ff.
Multigrid method, avoid SOR 866
Multigrid method, boundary conditions 868f.
Multigrid method, choice of operators 868
Multigrid method, coarse-grid correction 864f.
Multigrid method, coarse-to-fine operator 864 1337
Multigrid method, cycle 865
Multigrid method, dual viewpoint 875
Multigrid method, fine-to-coarse operator 864 1337
Multigrid method, full approximation storage (FAS) algorithm 874 1339ff.
Multigrid method, full multigrid method (FMG) 863 868 1334ff.
Multigrid method, full weighting 867
Multigrid method, Gauss — Seidel relaxation 865f. 1338
Multigrid method, half weighting 867 1337
Multigrid method, importance of adjoint operator 867
Multigrid method, injection operator 864 1337
Multigrid method, interpolation operator 864 1337
Multigrid method, line relaxation 866
Multigrid method, local truncation error 875
Multigrid method, Newton’s rule 874 876 1339 1341
Multigrid method, nonlinear equations 874ff. 1339ff.
Multigrid method, nonlinear Gauss — Seidel relaxation 876 1341
Multigrid method, odd-even ordering 866 869 1338
Multigrid method, operation count 862
Multigrid method, prolongation operator 864 1337
Multigrid method, recursive nature 865 1009 1336
Multigrid method, relative truncation error 875
Multigrid method, relaxation as smoothing operator 865
Multigrid method, restriction operator 864 1337
Multigrid method, speeding up FMG algorithm 873
Multigrid method, stopping criterion 875f.
Multigrid method, straight injection 867
Multigrid method, symbol of operator 866f.
Multigrid method, use of Richardson extrapolation 869
Multigrid method, V-cycle 865 1336
Multigrid method, W-cycle 865 1336
Multigrid method, zebra relaxation 866
Multiple precision arithmetic 906ff. 1352ff.
Multiple roots 341 362
Multiplication, complex 171
Multiplication, multiple precision 907 909 1353f.
Multiplier of linear congruential generator 268
Multistep and multivalue methods (ODEs) 740ff. (see also Differential Equations; Predictor-corrector methods)
Multivariate normal distribution 690
Murphy’s Law 407
Musical scores 5f.
| NAG 1/xxiii 2/xx 26 64 205 454
Nag, Fortran 90 compiler 2/viii 2/xiv
Named constant 940
Named constant, for Numerical Recipes 1361
Named constant, initialization 1012
Named control structure 959 1219 1305
National Science Foundation (U.S.) 1/xvii 1/xix 2/ix
Natural cubic spline 109 1044f.
Navier — Stokes equation 830f.
nearest() intrinsic function 952 1146
Needle, eye of (minimization) 403
Negation, multiple precision 907 1353f.
Negentropy 811 896
Nelder and Mead DP, defined 937
Nelder — Mead minimization method 389 402 1208
Nested iteration 868
Neumann boundary conditions 820 840 851 858
Neutrino 640
Neville’s algorithm 102f. 105 134 182 1043
Newton — Cotes formulas 125ff. 140
Newton — Raphson method see Newton’s rule
Newton’s rule 143f. 180 341 355ff. 362 364 469 1059 1189
Newton’s rule, caution on use of numerical derivatives 356ff.
Newton’s rule, for matrix inverse 49 598
Newton’s rule, for reciprocal of number 911 1355
Newton’s rule, for square root of number 912 1356
Newton’s rule, fractal domain of convergence 360f.
Newton’s rule, globally convergent multidimensional 373 376ff. 382 749f. 752 1196 1199 1314f.
Newton’s rule, in multidimensions 370 372ff. 749f. 752 754 1194ff. 1314ff.
Newton’s rule, in nonlinear multigrid 874 876 1339 1341
Newton’s rule, nonlinear Volterra equations 787
Newton’s rule, safe 359 1190
Newton’s rule, scaling of variables 381
Newton’s rule, singular Jacobian 386
Newton’s rule, solving stiff ODEs 740
Newton’s rule, with backtracking 376 1196
Niederreiter sequence 300
NL2SOL 683
Noise bursty 889
Noise effect on maximum entropy method 567
Noise equivalent bandwidth 548
Noise fitting data which contains 647f. 650
Noise model, for optimal filtering 541
Nominal variable (statistics) 623
Non-interfering directions see Conjugate directions
Nonexpansive projection operator 805
Nonlinear eigenvalue problems 455
Nonlinear elliptic equations, multigrid method 874ff. 1339ff.
Nonlinear equations, in MEM inverse problems 813
Nonlinear equations, roots of 340ff.
Nonlinear instability 831
Nonlinear integral equations 781 787
Nonlinear programming 436
Nonnegativity constraints 423
Nonparametric statistics 633ff. 1277ff.
Nonpolynomial complete (NP-complete) 438
Norm, of matrix 50
Normal (Gaussian) distribution 267 652 682 798 1294
Normal (Gaussian) distribution, central limit theorem 652f.
Normal (Gaussian) distribution, deviates from 279f. 571 1152
Normal (Gaussian) distribution, kurtosis of 607
Normal (Gaussian) distribution, multivariate 690
Normal (Gaussian) distribution, semi-invariants of 608
Normal (Gaussian) distribution, tails compared to Poisson 653
Normal (Gaussian) distribution, two-dimensional (binormal) 631
Normal (Gaussian) distribution, variance of skewness of 606
Normal equations (fitting) 26 645 666ff. 795 800 1288
Normal equations (fitting), often are singular 670
Normalization of Bessel functions 175
Normalization of floating-point representation 19 882 1343
Normalization of functions 142 765
Normalization of modified Bessel functions 232
not() intrinsic function 951
Notch filter 551 555f.
NP-complete problem 438
nr.f90 (module file) 936 1362 1384ff.
nrerror()utility function 989 995
nrtype.f90 (module file) 936f.
nrtype.f90 (module file), named constants 1361
nrutil.f90 (module file) 936 1070 1362 1364ff.
nrutil.f90 (module file), table of contents 1364
Null hypothesis 603
nullify statement 953f. 1070 1302
Nullity 53
NullSpace 25 53f. 449 795
Number-theoretic transforms 503f.
Numeric inquiry functions 2/xiv 1107 1231 1343
Numerical derivatives 180ff. 645 1075
Numerical integration see Quadrature
Numerical intrinsic functions 946 951f.
Numerical Recipes Software 1/xv 1/xxiiff. 2/xviiff.
Numerical Recipes Software, address and fax number 1/iv 1/xxii 2/iv 2/xix
Numerical Recipes Software, Web home page 1/xx 2/xvii
Numerical Recipes, as trademark 1/xxiii 2/xx
Numerical Recipes, compatibility with First Edition 4
Numerical Recipes, Example Book 3
Numerical Recipes, Fortran 90 types 936f. 1361
Numerical Recipes, how to get programs 1/xx 2/xvii
Numerical Recipes, how to report bugs 1/iv 2/iv
Numerical Recipes, interface blocks (Fortran 90) 937 941f. 1084 1384ff.
Numerical Recipes, no warranty on 1/xx 2/xvii
Numerical Recipes, plan of two-volume edition 1/xiii
Numerical Recipes, table of dependencies 921ff. 1434ff.
Numerical Recipes, utility functions (Fortran 90) 936f. 945 968 970 972ff. 977 984 987ff. 1015 1071f. 1361ff.
Nyquist frequency 494ff. 520 543 545 569ff.
Nystrom method 782f. 789 1325
Nystrom method, product version 789 1331
Object extensibility 8
Object-Oriented Programming 2/xvi 2 8
Objective function 424
Oblateness parameter 764
Obsolete features see Fortran Obsolescent
Octal constant, initialization 959
Odd parity 888
Odd-even ordering, allows parallelization 1333
Odd-even ordering, in Gauss — Seidel relaxation 866 869 1338
Odd-even ordering, in successive over-relaxation (SOR) 859 1332
OEM information 1/xxii
One-sided power spectral density 492
ONLY option, for USE statement 941 957 1067
Operation count, balancing 476
Operation count, Bessel function evaluation 228
Operation count, bisection method 346
Operation count, Cholesky decomposition 90
Operation count, coefficients of interpolating polynomial 114f.
Operation count, complex multiplication 97
Operation count, cubic spline interpolation 109
Operation count, evaluating polynomial 168
Operation count, fast Fourier transform (FFT) 498
Operation count, Gauss — Jordan elimination 34 39
Operation count, Gaussian elimination 34
Operation count, Givens reduction 463
Operation count, Householder reduction 467
Operation count, interpolation 100
Operation count, inverse iteration 488
Operation count, iterative improvement 48
Operation count, Jacobi transformation 460
Operation count, Kendall’s tau 637
Operation count, linear congruential generator 268
Operation count, LU decomposition 36 39
Operation count, matrix inversion 97
Operation count, matrix multiplication 96
Operation count, maximum entropy method 567
Operation count, multidimensional minimization 413f.
Operation count, multigrid method 862
Operation count, multiplication 909
Operation count, polynomial evaluation 97f. 168
Operation count, QL method 470 473
Operation count, QR decomposition 92
Operation count, QR method for Hessenberg matrices 484
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