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| Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in Fortran 90 |
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| Предметный указатель |
cumprod() utility function 974 988 997 1072 1086
cumsum()utility function 974 989 997 1280 1305
Cumulant, of a polynomial 977 999 1071f. 1192
Cumulative binomial distribution 222f.
Cumulative Poisson function 214
Cumulative Poisson function, related to incomplete gamma function 214
Curvature matrix see Hessian matrix
cycle statement 959 1219
Cycle, in multigrid method 865
Cyclic Jacobi method 459 1225
Cyclic reduction (CR) 848f. 852ff.
Cyclic reduction (CR), linear recurrences 974
Cyclic reduction (CR), tridiagonal systems 976 1018
Cyclic redundancy check (CRC) 888ff. 1344f.
Cyclic tridiagonal systems 67 1030
D.C. (direct current) 492
Danielson — Lanczos lemma 498f. 525 1235ff.
DAP Fortran 2/xi
Data compression 596f. 881
Data compression, arithmetic coding 902ff. 1349ff.
Data compression, cosine transform 513
Data compression, Huffman coding 896f. 902 1346ff.
Data compression, linear predictive coding (LPC) 563ff.
Data compression, lossless 896
Data Encryption Standard (DES) 290ff. 1144 1147f. 1156ff.
Data hiding 956ff. 1209 1293 1296
Data parallelism 941 964ff. 985
DATA statement 959
DATA statement, for binary, octal, hexadecimal constants 959
DATA statement, repeat count feature 959
DATA statement, superseded by initialization expression 943 959 1127
Data type 18 936
Data type, accuracy parameters 1362f.
Data type, Character 1183
Data type, derived 2/xiii 937 1030 1336 1346
Data type, derived, for array of arrays 956 1336
Data type, derived, for Numerical Recipes 1361
Data type, derived, initialization 2/xv
Data type, derived, storage allocation 955
Data type, DP (double precision) 1361f.
Data type, DPC (double precision complex) 1361
Data type, IfB (4 byte integer) 1361
Data type, intrinsic 937
Data type, IoB (1 byte integer) 1361
Data type, ItB (2 byte integer) 1361
Data type, LGT (default logical type) 1361
Data type, nrtype.f90 1361f.
Data type, passing complex as real 1140
Data type, SP (single precision) 1361f.
Data type, SPC (single precision complex) 1361
Data type, user-defined 1346
Data, assigning keys to 889
Data, continuous vs. binned 614
Data, entropy 626ff. 896 1275
Data, essay on 603
Data, fitting 650ff. 1285ff.
Data, fraudulent 655
Data, glitches in 653
Data, iid (independent and identically distributed) 686
Data, modeling 650ff. 1285ff.
Data, serial port 892
Data, smoothing 604 644ff. 1283f.
Data, statistical tests 603ff. 1269ff.
Data, unevenly or irregularly sampled 569 574 648f. 1258ff.
Data, use of CRCs in manipulating 889
Data, windowing 545ff. 1254
DAUB12 598
DAUB20 590f. 1265
DAUB4 584ff. 588 590f. 594 1264f.
DAUB6 586
Daubechies wavelet coefficients 584ff. 588 590f. 594 598 1264ff.
Davidon — Fletcher — Powell algorithm 390 418ff. 1215
Dawson’s integral 252ff. 600 1127f.
Dawson’s integral, approximation for 252f.
Dawson’s integral, routine for 253f. 1127
dble() intrinsic function (deprecated) 947
deallocate statement 938f. 953f. 1197 1266 1293
Deallocation, of allocatable array 938 953f. 1197 1266 1293
Debugging 8
DEC (Digital Equipment Corp.) 1/xxiii 2/xix 886
DEC (Digital Equipment Corp.), Alpha AXP 2/viii
DEC (Digital Equipment Corp.), Fortran 90 compiler 2/viii
DEC (Digital Equipment Corp.), quadruple precision option 1362
DEC (Digital Equipment Corp.), VAX 4
Decomposition see Cholesky decomposition; LU decomposition; QR decomposition; Singular value decomposition (SVD)
Deconvolution 535 540 1253
Defect, in multigrid method 863
Deferred approach to the limit see Richardson’s deferred approach to the limit
Deflation of matrix 471
Deflation of polynomials 362ff. 370f. 977
Degeneracy of linear algebraic equations 22 53 57 670
Degenerate kernel 785
Degenerate minimization principle 795
Degrees of freedom 615f. 654 691
Dekker, T.J. 353
Demonstration programs 3 936
Deprecated features, common block 2/xif. 940 953 957 1067 1298 1320 1322 1324 1330
Deprecated features, dble() intrinsic function 947
Deprecated features, EQUIVALENCE statement 2/xif. 1161 1286
Deprecated features, statement function 1057 1256
Derivatives, computation via Chebyshev approximation 183 189 1077f.
Derivatives, computation via Savitzky — Golay filters 183 645
Derivatives, matrix of first partial see Jacobian determinant
Derivatives, matrix of second partial see Hessian matrix
Derivatives, numerical computation 180ff. 379 645 732 750 771 1075 1197 1309
Derivatives, of polynomial 167 978 1071f.
Derivatives, use in optimization 388f. 399 1205ff.
Derived data type see Data type derived
DES see Data Encryption Standard
Descending transformation, elliptic integrals 256
Descent direction 376 382 419
Descriptive statistics 603ff. 1269ff.
Design matrix 645 665 795 801 1082
Determinant 25 41
Deviates, random see Random deviates
DFP algorithm see Davidon — Fletcher — Powell algorithm
diagadd() utility function 985 989 1004
diagmult() utility function 985 989 1004 1294
Diagonal dominance 43 679 780 856
Difference equations, finite see Finite difference equations (FDEs)
Difference operator 161
Differential equations 701f. 1297ff.
Differential equations, accuracy vs. stability 704 729
Differential equations, Adams — Bashforth — Moulton schemes 741
Differential equations, adaptive stepsize control 703 708ff. 719 726 731 737 742f. 1298ff. 1303ff. 1308f. 1311ff.
Differential equations, algebraically difficult sets 763
Differential equations, backward Euler’s method 729
Differential equations, Bader — Deuflhard method for stiff 730 735 1310f.
Differential equations, boundary conditions 701f. 745ff. 749 751f. 771 1314ff.
Differential equations, Bulirsch — Stoer method 202 263 702 706 716 718ff. 740 1138 1303
Differential equations, Bulirsch — Stoer method for conservative equations 726 1307
Differential equations, comparison of methods 702f. 739f. 743
Differential equations, conservative 726 1307
Differential equations, danger of too small stepsize 714
Differential equations, eigenvalue problem 748 764ff. 770ff. 1319ff.
Differential equations, embedded Runge — Kutta method 709f. 731 1298 1308
Differential equations, equivalence of multistep and multivalue methods 743
Differential equations, Euler’s method 702 704 728f.
Differential equations, forward Euler’s method 728
Differential equations, free boundary problem 748 776
Differential equations, high-order implicit methods 730ff. 1308ff.
Differential equations, implicit differencing 729 740 1308
Differential equations, initial value problems 702
Differential equations, internal boundary conditions 775ff.
Differential equations, internal singular points 775ff.
Differential equations, interpolation on right-hand sides 111
Differential equations, Kaps — Rentrop method for stiff 730 1308
Differential equations, local extrapolation 709
Differential equations, modified midpoint method 716f. 719 1302f.
Differential equations, multistep methods 740ff.
| Differential equations, multivalue methods 740
Differential equations, order of method 704f. 719
Differential equations, path integration for function evaluation 201ff. 263 1138
Differential equations, predictor-corrector methods 702 730 740ff.
Differential equations, r.h.s. independent of x 729f.
Differential equations, reduction to first-order sets 701 745
Differential equations, relaxation method 746f. 753ff. 1316ff.
Differential equations, relaxation method, example of 764ff. 1319ff.
Differential equations, Rosenbrock methods for stiff 730 1308f.
Differential equations, Runge — Kutta method 702 704ff. 708ff. 731 740 1297f. 1308
Differential equations, Runge — Kutta method, high-order 705 1297
Differential equations, Runge — Kutta — Fehlberg method 709ff. 1298
Differential equations, scaling stepsize to required accuracy 709
Differential equations, second order 726 1307
Differential equations, semi-implicit differencing 730
Differential equations, semi-implicit Euler method 730 735f.
Differential equations, semi-implicit extrapolation method 730 735f. 1311ff.
Differential equations, semi-implicit midpoint rule 735f. 13
Differential equations, shooting method 746 749ff. 1314ff.
Differential equations, shooting method, example 770ff. 1321ff.
Differential equations, similarity to Volterra integral equations 786
Differential equations, singular points 718f. 751 775ff. 1315f. 1323ff.
Differential equations, step doubling 708f.
Differential equations, stepsize control 703 708ff. 719 726 731 737 742f. 1298 1303ff. 1308f.
Differential equations, stiff 703 727ff. 1308ff.
Differential equations, stiff methods compared 739
Differential equations, Stoermer’s rule 726 1307
Diffusion equation 818 838ff. 855
Diffusion equation, Crank — Nicolson method 840 844 846
Diffusion equation, Forward Time Centered Space (FTCS) 839ff. 855
Diffusion equation, implicit differencing 840
Diffusion equation, multidimensional 846
Digamma function 216
Digital filtering see Filter
Dihedral group  894
dim optional argument 948
Dimensional expansion 965ff.
Dimensions (units) 678
Diminishing increment sort 322 1168
Dirac delta function 284 780
Direct method see Periodogram
Direct methods for linear algebraic equations 26 1014
Direct product see Outer product of matrices
Direction numbers, Sobol’s sequence 300
Direction of largest decrease 410f.
Direction-set methods for minimization 389 406f. 1210ff.
Dirichlet boundary conditions 820 840 850 856 858
Disclaimer of warranty 1/xx 2/xvii
Discordant pair for Kendall’s tau 637 1281
Discrete convolution theorem 531f.
Discrete Fourier transform (DFT) 495ff. 1235ff.
Discrete Fourier transform (DFT) as approximate continuous transform 497 (see also Fast Fourier transform (FFT))
Discrete optimization 436ff. 1219ff.
Discriminant 178 457
Diskettes are ANSI standard 3
Diskettes, how to order 1/xxi 2/xvii
dispersion 831
DISPO see Savitzky — Golay filters
Dissipation, numerical 830
Divergent series 161
Divide and conquer algorithm 1226 1229
Division, complex 171
Division, multiple precision 910f. 1356
Division, of polynomials 169 362 370 1072
dn function 261 1137f.
Do-list, implied 968 971 1127
Do-loop 2/xiv
Do-until iteration 14
Do-while iteration 13
Dogleg step methods 386
Domain of integration 155f.
Dominant solution of recurrence relation 174
Dot (denotes matrix multiplication) 23
dot_product() intrinsic function 945 949 969 1216
Double exponential error distribution 696
Double precision, as refuge of scoundrels 882
Double precision, converting to 1362
Double precision, use in iterative improvement 47 1022
Double root 341
Downhill simplex method see Simplex method
Driver programs 3
Dual viewpoint, in multigrid method 875
Duplication theorem, elliptic integrals 256
DWT (discrete wavelet transform) see Wavelet transform
Dynamical allocation of storage 2/xiii 869 938 941f. 953ff. 1327 1336
Dynamical allocation of storage, garbage collection 956
Dynamical allocation of storage, increasing 955 1070 1302
Eardlcy, D.M. 338
EBCDIC 890
Economization of power series 192f. 195 1080
Eigensystems 449ff. 1225ff.
Eigensystems, and integral equations 779 785
Eigensystems, balancing matrix 476f. 1230f.
Eigensystems, bounds on eigenvalues 50
Eigensystems, calculation of few eigenvalues 454 488
Eigensystems, canned routines 454f.
Eigensystems, characteristic polynomial 449 469
Eigensystems, completeness 450
Eigensystems, defective 450 476 489
Eigensystems, deflation 471
Eigensystems, degenerate eigenvalues 449ff.
Eigensystems, elimination method 453 478 1231
Eigensystems, factorization method 453
Eigensystems, fast Givens reduction 463
Eigensystems, generalized eigenproblem 455
Eigensystems, Givens reduction 462f.
Eigensystems, Hermitian matrix 475
Eigensystems, Hessenberg matrix 453 470 476ff. 488 1232
Eigensystems, Householder transformation 453 462ff. 469 473 475 478 1227f. 1231
Eigensystems, ill-conditioned eigenvalues 477
Eigensystems, implicit shifts 472ff. 1228f.
Eigensystems, invariance under similarity transform 452
Eigensystems, inverse iteration 455 469 476 487ff. 1230
Eigensystems, Jacobi transformation 453 456ff. 462 475 489 1225f.
Eigensystems, left eigenvalues 451
Eigensystems, list of tasks 454f.
Eigensystems, multiple eigenvalues 489
Eigensystems, nonlinear 455
Eigensystems, nonsymmetric matrix 476ff. 1230ff.
Eigensystems, operation count of balancing 476
Eigensystems, operation count of Givens reduction 463
Eigensystems, operation count of Householder reduction 467
Eigensystems, operation count of inverse iteration 488
Eigensystems, operation count of Jacobi method 460
Eigensystems, operation count of QL method 470 473
Eigensystems, operation count of QR method for Hessenberg matrices 484
Eigensystems, operation count of reduction to Hessenberg form 479
Eigensystems, orthogonality 450
Eigensystems, parallel algorithms 1226 1229
Eigensystems, polynomial roots and 368 1193
Eigensystems, QL method 469ff. 475 488f.
Eigensystems, QL method with implicit shifts 472ff. 1228f.
Eigensystems, QR method 52 453 456 469ff. 1228
Eigensystems, QR method for Hessenberg matrices 480ff. 1232ff.
Eigensystems, real, symmetric matrix 150 467 785 1225 1228
Eigensystems, reduction to Hessenberg form 478f. 1231
Eigensystems, right eigenvalues 451
Eigensystems, shifting eigenvalues 449 470f. 480
Eigensystems, special matrices 454
Eigensystems, termination criterion 484 488
Eigensystems, tridiagonal matrix 453 469ff. 488 1228
Eigenvalue and eigenvector, defined 449
Eigenvalue problem for differential equations 748 764ff. 770ff. 1319ff.
Eigenvalues and polynomial root finding 368 1193
EISPACK 454
Electromagnetic potential 519
ELEMENTAL attribute (Fortran 95) 961 1084
Elemental functions 2/xiii 2/xv 940 942 946f. 961 986 1015 1083 1097f.
Elimination see Gaussian elimination
Ellipse in confidence limit estimation 688
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