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| Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in Fortran 90 |
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| Предметный указатель |
Elliptic integrals 254ff. 906
Elliptic integrals, addition theorem 255
Elliptic integrals, Carlson’s forms and algorithms 255f. 1128ff.
Elliptic integrals, Cauchy principal value 256f.
Elliptic integrals, duplication theorem 256
Elliptic integrals, Legendre 254ff. 260f. 1135ff.
Elliptic integrals, routines for 257ff. 1128ff.
Elliptic integrals, symmetric form 255
Elliptic integrals, Weierstrass 255
Elliptic partial differential equations 818 1332ff.
Elliptic partial differential equations, alternating-direction implicit method (ADI) 861f. 906
Elliptic partial differential equations, analyze/factorize/operate package 824
Elliptic partial differential equations, biconjugate gradient method 824
Elliptic partial differential equations, boundary conditions 820
Elliptic partial differential equations, comparison of rapid methods 854
Elliptic partial differential equations, conjugate gradient method 824
Elliptic partial differential equations, cyclic reduction 848f. 852ff.
Elliptic partial differential equations, Fourier analysis and cyclic reduction (FACR) 848ff. 854
Elliptic partial differential equations, Gauss — Seidel method 855 864ff. 876 1338 1341
Elliptic partial differential equations, incomplete Cholesky conjugate gradient method (ICCG) 824
Elliptic partial differential equations, Jacobi’s method 855f. 864
Elliptic partial differential equations, matrix methods 824
Elliptic partial differential equations, multigrid method 824 862ff. 1009 1334ff.
Elliptic partial differential equations, rapid (Fourier) method 824 848ff.
Elliptic partial differential equations, relaxation method 823 854ff. 1332
Elliptic partial differential equations, strongly implicit procedure 824
Elliptic partial differential equations, successive over-relaxation (SOR) 857ff. 862 866 1332
elsewhere construct 943
Emacs, GNU 1/xvi
Embedded Runge — Kutta method 709f. 731 1298 1308
Encapsulation, in programs 7
Encryption 290 1156
enddo statement 12 17
entropy 896
Entropy of data 626ff. 811 1275
EOM (end of message) 902
eoshift() intrinsic function 950
eoshift() intrinsic function, communication bottleneck 969
eoshift() intrinsic function, vector shift argument 1019f.
eoshift() intrinsic function, vs. array section 1078
epsilon() intrinsic function 951 1189
Equality constraints 423
Equations, cubic 178ff. 360
Equations, normal (fitting) 645 666ff. 800 1288
Equations, quadratic 20 178
Equivalence classes 337f. 1180
EQUIVALENCE statement 2/xif. 1161 1286
Equivalence transformation 166
Error function 213f. 601 1094f.
Error function, approximation via sampling theorem 601
Error function, Chebyshev approximation 214 1095
Error function, complex 252
Error function, for Fisher’s z-transformation 632 1276
Error function, for significance of correlation 631 1276
Error function, for sum squared difference of ranks 635 1277
Error function, relation to Dawson’s integral 252 1127
Error function, relation to Fresnel integrals 248
Error function, relation to incomplete gamma function 213
Error function, routine for 214 1094
Error handling in programs 2/xii 2/xvi 3 994f. 1036 1370f.
Error, checksums for preventing 891
Error, clocking 891
Error, double exponential distribution 696
Error, in multigrid method 863
Error, local truncation 875
Error, Lorentzian distribution 696f.
Error, nonnormal 653 690 694ff.
Error, relative truncation 875
Error, roundoff 180f. 881 1362
Error, series, advantage of an even 132f. 717 1362
Error, systematic vs. statistical 653 1362
Error, truncation 20f. 180 399 709 881 1362
Error, varieties found by check digits 895
Error, varieties of, in PDEs 831f. (see also Roundoff error)
Estimation of parameters see Fitting; Maximum likelihood estimate
Estimation of power spectrum 542ff. 565ff. 1254ff. 1258
Euler equation (fluid flow) 831
Euler — Maclaurin summation formula 132 135
Euler’s constant 216ff. 250
Euler’s method for differential equations 702 704 728f.
Euler’s transformation 160f. 1070
Euler’s transformation, generalized form 162f.
Evaluation of functions see Function
Even and odd parts, of continued fraction 166 211 216
Even parity 888
Exception handling in programs see Error handling in programs
Exit statement 959 1219
Explicit differencing 827
Exponent in floating point format 19 882 1343
exponent intrinsic function 1107
Exponential deviate 278 1151f.
Exponential integral 215ff. 1096f.
Exponential integral, asymptotic expansion 218
Exponential integral, continued fraction 216
Exponential integral, recurrence relation 172
Exponential integral, related to incomplete gamma function 215
Exponential integral, relation to cosine integral 250
Exponential integral, routine for  217 1096
Exponential integral, routine for Ei( ) 218 1097
Exponential integral, series 216
Exponential probability distribution 570
Extended midpoint rule 124f. 129f. 135 1054f.
Extended Simpson’s rule 128 788 790
Extended Simpson’s three-eighths rule 789
Extended trapezoidal rule 125 127 130ff. 135 786 1052ff. 1326
Extended trapezoidal rule, roundoff error 132
Extirpolation (so-called) 574 1261
Extrapolation 99ff.
Extrapolation, by linear prediction 557ff. 1256f.
Extrapolation, differential equations 702
Extrapolation, for Romberg integration 134 (see also Interpolation)
Extrapolation, in Bulirsch — Stoer method 718ff. 726 1305ff.
Extrapolation, local 709
Extrapolation, maximum entropy method as type of 567
Extrapolation, polynomial 724 726 740 1305f.
Extrapolation, rational function 718ff. 726 1306f.
Extrapolation, relation to interpolation 101
Extremization see Minimization
F-distribution probability function 222
F-test for differences of variances 611 613 1271
FACR see Fourier analysis and cyclic reduction (FACR)
Facsimile standard 901
Factorial, double (denoted “!!”) 247
Factorial, evaluation of 159 1072 1086
Factorial, relation to gamma function 206
Factorial, routine for 207f. 1086ff.
False position 347ff. 1185f.
Family tree 338
FAS (full approximation storage algorithm) 874 1339ff.
Fast Fourier transform (FFT) 498ff. 881 981 1235f.
Fast Fourier transform (FFT), alternative algorithms 503f.
Fast Fourier transform (FFT), and Clenshaw — Curtis quadrature 190
Fast Fourier transform (FFT), as approximation to continuous transform 497
Fast Fourier transform (FFT), at double frequency 575
Fast Fourier transform (FFT), Bartlett window 547 1254
Fast Fourier transform (FFT), bit reversal 499f. 525
Fast Fourier transform (FFT), column-parallel algorithm 981 1237ff.
Fast Fourier transform (FFT), communication bottleneck 969 981 1250
Fast Fourier transform (FFT), convolution 503f. 523 531f. 909 1253 1354
Fast Fourier transform (FFT), convolution of large data sets 536f.
Fast Fourier transform (FFT), Cooley — Tukey algorithm 503 1250
Fast Fourier transform (FFT), Cooley — Tukey algorithm, parallel 1239f.
Fast Fourier transform (FFT), correlation 538f. 1254
Fast Fourier transform (FFT), cosine transform 190 511f. 851 1245f.
Fast Fourier transform (FFT), cosine transform, second form 513 852 1246
Fast Fourier transform (FFT), Danielson — Lanczos lemma 498f. 525
Fast Fourier transform (FFT), data sets not a power of 2 503
Fast Fourier transform (FFT), data smoothing 645
Fast Fourier transform (FFT), data windowing 545ff. 1254
Fast Fourier transform (FFT), decimation-in-frequency algorithm 503
| Fast Fourier transform (FFT), decimation-in-time algorithm 503
Fast Fourier transform (FFT), discrete autocorrelation 539 1254
Fast Fourier transform (FFT), discrete convolution theorem 531f.
Fast Fourier transform (FFT), discrete correlation theorem 538
Fast Fourier transform (FFT), effect of caching 982
Fast Fourier transform (FFT), endpoint corrections 578f. 1261ff.
Fast Fourier transform (FFT), external storage 525
Fast Fourier transform (FFT), figures of merit for data windows 548
Fast Fourier transform (FFT), filtering 551f.
Fast Fourier transform (FFT), FIR filter 553
Fast Fourier transform (FFT), for multiple precision arithmetic 906
Fast Fourier transform (FFT), for multiple precision multiplication 909 1354
Fast Fourier transform (FFT), for quadrature 124
Fast Fourier transform (FFT), four-step framework 983 1239
Fast Fourier transform (FFT), Fourier integrals 577ff. 1261
Fast Fourier transform (FFT), Fourier integrals, infinite range 583
Fast Fourier transform (FFT), Hamming window 547
Fast Fourier transform (FFT), Hann window 547
Fast Fourier transform (FFT), history 498
Fast Fourier transform (FFT), HR filter 553ff.
Fast Fourier transform (FFT), image processing 803 805
Fast Fourier transform (FFT), integrals using 124
Fast Fourier transform (FFT), inverse of cosine transform 512ff.
Fast Fourier transform (FFT), inverse of sine transform 511
Fast Fourier transform (FFT), large data sets 525
Fast Fourier transform (FFT), leakage 544
Fast Fourier transform (FFT), memory-local algorithm 528
Fast Fourier transform (FFT), multidimensional 515ff. 1236f. 1241 1246 1251
Fast Fourier transform (FFT), number-theoretic transforms 503f.
Fast Fourier transform (FFT), of real data in 2D and 3D 519ff. 1248f.
Fast Fourier transform (FFT), of real functions 504ff. 519ff. 1242f. 1248f.
Fast Fourier transform (FFT), operation count 498
Fast Fourier transform (FFT), optimal (Wiener) filtering 539ff. 558
Fast Fourier transform (FFT), order of storage in 501
Fast Fourier transform (FFT), parallel algorithms 981f. 1235ff.
Fast Fourier transform (FFT), partial differential equations 824 848ff.
Fast Fourier transform (FFT), Parzen window 547
Fast Fourier transform (FFT), periodicity of 497
Fast Fourier transform (FFT), periodogram 543ff. 566
Fast Fourier transform (FFT), power spectrum estimation 542ff. 1254ff.
Fast Fourier transform (FFT), related algorithms 503f.
Fast Fourier transform (FFT), row-parallel algorithm 981 1235f.
Fast Fourier transform (FFT), Sande — Tukey algorithm 503
Fast Fourier transform (FFT), sine transform 508ff. 850 1245
Fast Fourier transform (FFT), Singleton’s algorithm 525
Fast Fourier transform (FFT), six-step framework 983 1240
Fast Fourier transform (FFT), square window 546 1254
Fast Fourier transform (FFT), timing 982
Fast Fourier transform (FFT), treatment of end effects in convolution 533
Fast Fourier transform (FFT), treatment of end effects in correlation 538f.
Fast Fourier transform (FFT), Tukey’s trick for frequency doubling 575
Fast Fourier transform (FFT), use in smoothing data 645
Fast Fourier transform (FFT), used for Lomb periodogram 574 1259
Fast Fourier transform (FFT), variance of power spectrum estimate 544f. 549
Fast Fourier transform (FFT), virtual memory machine 528
Fast Fourier transform (FFT), Welch window 547 1254
Fast Fourier transform (FFT), Winograd algorithms 503 (see also Discrete Fourier transform (DFT); Fourier transform; Spectral density)
Faure sequence 300
Fax (facsimile) Group 3
Feasible vector 424
FFT see Fast Fourier transform (FFT)
Field, in data record 329
Figure-of-merit function 650
Filon’s method 583
Filter 551f.
Filter, acausal 552
Filter, bilinear transformation method 554
Filter, by fast Fourier transform (FFT) 523 551f.
Filter, causal 552 644
Filter, characteristic polynomial 554
Filter, data smoothing 644f. 1283f.
Filter, digital 551f.
Filter, DISPO 644
Filter, finite impulse response (FIR) 531 552
Filter, homogeneous modes of 554
Filter, in the time domain 551f.
Filter, infinite impulse response (HR) 552ff. 566
Filter, Kalman 700
Filter, linear 552ff.
Filter, low-pass for smoothing 644ff. 1283f.
Filter, nonrecursive 552
Filter, optimal (Wiener) 535 539ff. 558 644
Filter, quadrature mirror 585 593
Filter, realizable 552 554f.
Filter, recursive 552ff. 566
Filter, Remes exchange algorithm 553
Filter, Savitzky — Golay 183 644ff. 1283f.
Filter, stability of 554f.
Fine-to-coarse operator 864 1337
Finite difference equations (FDEs) 753 763 774
Finite difference equations (FDEs), altemating-direction implicit method (ADI) 847 861f.
Finite difference equations (FDEs), art not science 829
Finite difference equations (FDEs), Cayley’s form for unitary operator 844
Finite difference equations (FDEs), Courant condition 829 832ff. 836
Finite difference equations (FDEs), Courant condition (multidimensional) 846
Finite difference equations (FDEs), Crank — Nicolson method 840 844 846
Finite difference equations (FDEs), eigenmodes of 827f.
Finite difference equations (FDEs), explicit vs. implicit schemes 827
Finite difference equations (FDEs), forward Euler 826f.
Finite difference equations (FDEs), Forward Time Centered Space (FTCS) 827ff. 839ff. 843 855
Finite difference equations (FDEs), implicit scheme 840
Finite difference equations (FDEs), in relaxation methods 753ff.
Finite difference equations (FDEs), Lax method 828ff. 836
Finite difference equations (FDEs), Lax method (multidimensional) 845f.
Finite difference equations (FDEs), mesh drifting instability 834f.
Finite difference equations (FDEs), numerical derivatives 181
Finite difference equations (FDEs), partial differential equations 821f.
Finite difference equations (FDEs), staggered leapfrog method 833f.
Finite difference equations (FDEs), two-step Lax — Wendroff method 835ff.
Finite difference equations (FDEs), upwind differencing 832f. 837
Finite element methods, partial differential equations 824
Finite impulse response (FIR) 531
Finkelstein, S. 1/xvi 2/ix
FIR (finite impulse response) filter 552
Fisher’s z-transformation 631f. 1276
Fitting 650ff. 1285ff.
Fitting, an exponential 674
Fitting, basis functions 665
Fitting, by Chebyshev approximation 185f. 1076
Fitting, by rational Chebyshev approximation 197ff. 1081f.
Fitting, chi-square 653ff. 1285ff.
Fitting, confidence levels from singular value decomposition (SVD) 693f.
Fitting, confidence levels related to chi-square values 691f.
Fitting, confidence limits on fitted parameters 684ff.
Fitting, covariance matrix not always meaningful 651 690
Fitting, degeneracy of parameters 674
Fitting, freezing parameters in 668 700
Fitting, Gaussians, a sum of 682 1294
Fitting, general linear least squares 665ff. 1288 1290f.
Fitting, K-S test, caution regarding 621f.
Fitting, Kalman filter 700
Fitting, least squares 651f. 1285
Fitting, Legendre polynomials 674 1291f.
Fitting, Levenberg — Marquardt method 678ff. 816 1292f.
Fitting, linear regression 655ff. 1285ff.
Fitting, maximum likelihood estimation 652f. 694ff.
Fitting, Monte Carlo simulation 622 654 684ff.
Fitting, multidimensional 675
Fitting, nonlinear models 675ff. 1292f.
Fitting, nonlinear models, advanced methods 683
Fitting, nonlinear problems that are linear 674
Fitting, nonnormal errors 656 690 694ff.
Fitting, of sharp spectral features 566
Fitting, polynomial 83 114 191 645 665 674 1078 1291
Fitting, robust methods 694ff. 1294
Fitting, standard (probable) errors on fitted parameters 657f. 661 667 671 684ff. 1285f. 1288 1290
Fitting, straight line 655ff. 667f. 698 1285ff. 1294ff.
Fitting, straight line, errors in both coordinates 660ff. 1286ff.
Five-point difference star 867
Fixed point format 18
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