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| Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in Fortran 90 |
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| Предметный указатель |
(MEM) Memory leak 953 956 1071 1327
(SVD) swap() utility function 987 990f. 1015 1210
(SVD) swap() utility function 987 990f. 1015 1210
Abstract data types 2/xiii 1030
Accelerated convergence of series 160ff. 1070
Accuracy 19f.
Accuracy parameters 1362f.
Accuracy vs. stability 704 729 830 844
Accuracy, achievable in minimization 392 397 404
Accuracy, achievable in root finding 346f.
Accuracy, contrasted with fidelity 832 840
Accuracy, CPU different from memory 181
Acknowledgments 1/xvi 2/ix
Ada 2/x
Adams — Bashford — Moulton method 741
Adams’ stopping criterion 366
Adaptive integration 123 135 703 708ff. 720 726 731f. 737 742ff. 788 1298ff. 1303 1308f.
Adaptive integration, Monte Carlo 306ff. 1161ff.
Addition theorem, elliptic integrals 255
Addition, multiple precision 907 1353
ADI (alternating direction implicit) method 847 861f. 906
Adjoint operator 867
Adobe Illustrator 1/xvi 2/xx
Advective equation 826
AGM (arithmetic geometric mean) 906
Airy function 204 234 243f.
Airy function, routine for 244f. 1121
Aitken’s delta squared process 160
Aitken’s interpolation algorithm 102
Algol 2/x 2/xiv
Algorithms, non-numerical 881f. 1343ff.
Aliasing 495 569
all() intrinsic function 945 948
All-poles model 566 (see also Maximum entropy method (MEM))
All-zeros model 566 (see also Periodogram)
Allocatable array 938 941 952ff. 1197 1212 1266 1293 1306 1336
allocate statement 938f. 941 953f. 1197 1266 1293 1306 1336
allocated() intrinsic function 938 952ff. 1197 1266 1293
Allocation status 938 952ff. 961 1197 1266 1293
Alpha AXP 2/xix
Altemating-direction implicit method (ADI) 847 861f. 906
Alternating series 160f. 1070
Alternative extended Simpson’s rule 128
American National Standards Institute (ANSI) 2/x 2/xiii
Amoeba 403 (see also Simplex method
Amplification factor 828 830 832 840 845f.
Amplitude error 831
Analog-to-Digital Converter 812 886
Analyticity 195
Analyze/factorize/operate package 64 824
Anderson — Darling statistic 621
Andrew’s sine 697
Annealing, method of simulated 387f. 436ff. 1219ff.
Annealing, method of simulated, assessment 447
Annealing, method of simulated, for continuous variables 437 443ff. 1222
Annealing, method of simulated, schedule 438
Annealing, method of simulated, thermodynamic analogy 437
Annealing, method of simulated, traveling salesman problem 438ff. 1219ff.
ANSI (American National Standards Institute) 2/x 2/xiii
Antonov — Saleev variant of Sobol’ sequence 300 1160
any() intrinsic function 945 948
APL (computer language) 2/xi
Apple 1/xxiii
Apple Macintosh 2/xix 4 886
Approximate inverse of matrix 49
Approximation of functions 99 1043
Approximation of functions, by Chebyshev polynomials 185f. 513 1076ff.
Approximation of functions, by rational functions 197ff. 1081f.
Approximation of functions, by wavelets 594f. 782
Approximation of functions, Pad approximant 194ff. 1080f.
Argument checking 994f. 1086 1090 1092 1370f.
Argument, keyword 2/xiv 947f. 1341
Argument, optional 2/xiv 947f. 1092 1228 1230 1256 1272 1275 1340
Arithmetic arbitrary precision 881 906ff. 1352ff.
Arithmetic coding 881 902ff. 1349ff.
Arithmetic floating point 881 1343
Arithmetic IEEE standard 276 882 1343
Arithmetic progression 971f. 996 1072 1127 1365 1371f.
Arithmetic rounding 882 1343
Arithmetic-geometric mean (AGM) method 906
Arithmetic-if statement 2/xi
Array 953ff.
Array section 2/xiii 943ff. 960
Array section, matches by shape 944
Array section, pointer alias 939 944f. 1286 1333
Array section, skew 2/xii 945 960 985 1284
Array section, vs. eoshift 1078
Array, allocatable 938 941 952ff. 1197 1212 1266 1293 1306 1336
Array, allocated with pointer 941
Array, allocation 953
Array, array manipulation functions 950
Array, array sections 939 941 943ff.
Array, associated pointer 953f.
Array, assumed-shape 942
Array, automatic 938 954 1197 1212 1336
Array, centered subarray of 113
Array, conformable to a scalar 942f. 965 1094
Array, constructor 2/xii 968 971 1022 1052 1055 1127
Array, copying 991 1034 1327f. 1365f.
Array, cumulative product 997f. 1072 1086 1375
Array, cumulative sum 997 1280f. 1365 1375
Array, deallocation 938 953f. 1197 1266 1293
Array, disassociated pointer 953
Array, extents 938 949
Array, in Fortran ny 941
Array, increasing storage for 955 1070 1302
Array, index loss 967f.
Array, index table 1173ff.
Array, indices 942
Array, inquiry functions 948ff.
Array, intrinsic procedures 2/xiii 948ff.
Array, location of first “true” 993 1041 1369
Array, location of maximum value 993 1015 1017 1365 1369
Array, location of minimum value 993 1369f.
Array, manipulation functions 950 1247
Array, masked swapping of elements in two arrays 1368
Array, of arrays 2/xii 956 1336
Array, of length 0 944
Array, of length 1 949
Array, of pointers forbidden 956 1337
Array, operations on 942 949 964ff. 969 1026 1040 1050 1200 1326
Array, outer product 949 1076
Array, parallel features 941ff. 964ff. 985
Array, passing variable number of arguments to function 1022
Array, rank 938 949
Array, reallocation 955 992 1070f. 1365 1368f.
Array, reduction functions 948ff.
Array, shape 938 944 949
Array, size 938
Array, skew sections 945 985
Array, stride 944
Array, subscript bounds 942
Array, subscript triplet 944
Array, swapping elements of two arrays 991 1015 1365ff.
Array, target 938
Array, three-dimensional, in Fortran 90 1248
Array, transformational functions 948ff.
Array, unary and binary functions 949
Array, undefined status 952ff. 961 1266 1293
Array, zero-length 944
array_copy() utility function 988 991 1034 1153 1278 1328
arth() utility function 972 974 988 996 1072 1086 1127
arth() utility function, replaces do-list 968
Artificial viscosity 831 837
Ascending transformation, elliptic integrals 256
ASCII character set 6 888 896 902
Assembly language 269
assert() utility function 988 994 1086 1090 1249
assert_eq() utility function 988 995 1022
Associated Legendre polynomials 246ff. 764 1122f. 1319
| Associated Legendre polynomials, recurrence relation for 247
Associated Legendre polynomials, relation to Legendre polynomials 246
associated() intrinsic function 952f.
Association, measures of 604 622ff. 1275
Assumed-shape array 942
Asymptotic series 161
Asymptotic series, exponential integral 218
Attenuation factors 583 1261
Autocorrelation 492
Autocorrelation in linear prediction 558
Autocorrelation, use of FFT 538f. 1254
Autocorrelation, Wiener — Khinchin theorem 492 566f.
AUTODIN — II polynomial 890
Automatic array 938 954 1197 1212 1336
Automatic array, specifying size of 938 954
Automatic deallocation 2/xv 961
Autonomous differential equations 729f.
Autoregressive model (AR) see Maximum entropy method (MEM)
Average deviation of distribution 605 1269
Averaging kernel, in Backus — Gilbert method 807
Backsubstitution 33ff. 39 42 92 1017
Backsubstitution, complex equations 41
Backsubstitution, direct for computing  40
Backsubstitution, in band diagonal matrix 46 1021
Backsubstitution, in Cholesky decomposition 90 1039
Backsubstitution, in singular value decomposition 56 1022f.
Backsubstitution, relaxation solution of boundary value problems 755 1316
Backsubstitution, with QR decomposition 93 1040
Backtracking 419
Backtracking in quasi-Newton methods 376f. 1195
Backus — Gilbert method 806ff.
Backus, John 2/x
Backward deflation 363
Bader — Deuflhard method 730 735 1310f.
Bairstow’s method 364 370 1193
Balancing 476f. 1230f.
Band diagonal matrix 42ff. 1019
Band diagonal matrix, backsubstitution 46 1021
Band diagonal matrix, LU decomposition 45 1020
Band diagonal matrix, multiply by vector 44 1019
Band diagonal matrix, storage 44 1019
Band-pass filter 551 554f.
Band-pass filter wavelets 584 592f.
Bandwidth limited function 495
Bank accounts, checksum for 894
Bar codes, checksum for 894
Bartlett window 547 1254ff.
Base case, of recursive procedure 958
Base of representation 19 882 1343
BASIC, Numerical Recipes in 1 2/x 2/xviii
Basis functions in general linear least squares 665
Bayesian approach to inverse problems 799 810f. 816f.
Bayesian contrasted with frequentist 810
Bayesian views on straight line fitting 664
Bayesian vs. historic maximum entropy method 816f.
Bayes’ Theorem 810
Bays’ shuffle 270
Bernoulli number 132
Bessel functions 223ff. 234ff. 936 1101ff.
Bessel functions, asymptotic form 223f. 229f.
Bessel functions, complex 204
Bessel functions, continued fraction 234 239
Bessel functions, double precision 223
Bessel functions, fractional order 223 234ff. 1115ff.
Bessel functions, Miller’s algorithm 175 228 1106
Bessel functions, modified 229ff.
Bessel functions, modified, fractional order 239ff.
Bessel functions, modified, normalization formula 232 240
Bessel functions, modified, routines for 230ff. 1109ff.
Bessel functions, normalization formula 175
Bessel functions, parallel computation of 1107ff.
Bessel functions, recurrence relation 172 224 232 234
Bessel functions, reflection formulas 236
Bessel functions, reflection formulas, modified functions 241
Bessel functions, routines for 225ff. 236ff. llOlff.
Bessel functions, routines for modified functions 241ff. 1118
Bessel functions, series for 160 223
Bessel functions, series for  241
Bessel functions, series for  235
Bessel functions, spherical 234 245 1121f.
Bessel functions, turning point 234
Bessel functions, Wronskian 234 239
Best-fit parameters 650 656 660 698 1285ff.
beta function 206ff. 1089
BFGS algorithm see Broyden — Fletcher — Goldfarb — Shanno algorithm
Bias, of exponent 19
Bias, removal in linear prediction 563
Biconjugacy 77
Biconjugate gradient method, elliptic partial differential equations 824
Biconjugate gradient method, for sparse system 77 599 1034ff.
Biconjugate gradient method, preconditioning 78f. 824 1037
Bicubic interpolation 118f. 1049f.
Bicubic spline 120f. 1050f.
big-endian 293
Bilinear interpolation 117
Binary constant, initialization 959
Binomial coefficients 206ff. 1087f.
Binomial coefficients, recurrences for 209
Binomial probability function 208
Binomial probability function, cumulative 222f.
Binomial probability function, deviates from 281 285f. 1155
Binormal distribution 631 690
Biorthogonality 77
Bisection 111 359 1045f.
Bisection, compared to minimum bracketing 390ff.
Bisection, minimum finding with derivatives 399
Bisection, root finding 343 346f. 352f. 390 469 1184f.
BISYNCH 890
Bit 18
Bit manipulation functions see Bitwise logical functions
Bit reversal in fast Fourier transform (FFT) 499f. 525
Bitwise logical functions 2/xiii 17 287 890f. 951
bit_size() intrinsic function 951
Block of statements 7
Block-by-block method 788
Bode’s rule 126
Boltzmann probability distribution 437
Boltzmann’s constant 437
Bootstrap method 686f.
Bordering method for Toeplitz matrix 85f.
Borwein and Borwein method for  906 1357
Boundary 155f. 425f. 745
Boundary conditions for differential equations 701f.
Boundary conditions for spheroidal harmonics 764
Boundary conditions in multigrid method 868f.
Boundary conditions initial value problems 702
Boundary conditions partial differential equations 508 819ff. 848ff.
Boundary conditions two-point boundary value problems 702 745ff. 1314ff.
Boundary value problems see Differential equations; Elliptic partial differential equations; Two-point boundary value problems
Box — Muller algorithm for normal deviate 279f. 1152
Bracketing of function minimum 343 390ff. 402 1201f.
Bracketing of roots 341 343ff. 353f. 362 364 369 390 1183f.
Branch cut, for hypergeometric function 203
Branching 9
Break iteration 14
Brenner, N.M. 500 517
Brent’s method, minimization 389 395ff. 660f. 1204ff. 1286
Brent’s method, minimization, using derivative 389 399 1205
Brent’s method, root finding 341 349 660f. 1188f. 1286
Broadcast (parallel capability) 965ff.
Broyden — Fletcher — Goldfarb — Shanno algorithm 390 418ff. 1215
Broyden’s method 373 382f. 386 1199f.
Broyden’s method, singular Jacobian 386
btest() intrinsic function 951
Bubble sort 321 1168
Bugs 4
Bugs in compilers 1/xvii
Bugs, how to report 1/iv 2/iv
Bulirsch — Stoer algorithm for rational function interpolation 105f. 1043
Bulirsch — Stoer for second order equations 726 1307
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