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| Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in FORTRAN77 |
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| Предметный указатель |
Sine function evaluated from tan  173
Sine integral 248 250ff. 1123 1125f.
Sine integral continued fraction 250
Sine integral series 250 (see also “Cosine integral”)
Sine transform see “Fast Fourier transform (FFT)”; “Fourier transform”
Singleton’s algorithm for FFT 525
Singular value decomposition (SVD) 23 25 51ff. 1022
Singular value decomposition (SVD), and bases for nullspace and range 53
Singular value decomposition (SVD), and least squares 54ff. 199f. 668 670ff. 1081 1290f.
Singular value decomposition (SVD), and rational Chebyshev approximation 199f. 1081f.
Singular value decomposition (SVD), approximation of matrices 58f.
Singular value decomposition (SVD), backsubstitution 56 1022f.
Singular value decomposition (SVD), confidence levels from 693f.
Singular value decomposition (SVD), covariance matrix 693f.
Singular value decomposition (SVD), fewer equations than unknowns 57
Singular value decomposition (SVD), for inverse problems 797
Singular value decomposition (SVD), in minimization 410
Singular value decomposition (SVD), more equations than unknowns 57f.
Singular value decomposition (SVD), of square matrix 53ff. 1023
Singular value decomposition (SVD), parallel algorithms 1026
Singular value decomposition (SVD), use for ill — conditioned matrices 56 58 449
Singular value decomposition (SVD), use for orthonormal basis 58 94
Singularities in integral equations 788ff. 1328
Singularities in integral equations, worked example 792 1328ff.
Singularities in integrands 135ff. 788 1055 1328ff.
Singularities of hypergeometric function 203 263
Singularities removal in numerical integration 137ff. 788 1057ff. 1328ff.
Singularity, subtraction of the 789
SIPSOL 824
Six-step framework, for FFT 983 1240
size() intrinsic function 938 942 945 948
Skew array section 2/xii 945 960 985 1284
Skewness of distribution 606 608 1269
Smoothing importance in multigrid method 865
Smoothing of data 114 644ff. 1283f.
Smoothing of data in integral equations 781
sn function 261 1137f.
Snyder, N.L. 1/xvi
Sobol’s quasi — random sequence 300ff. 1160f.
Sonata 9
Sonnet 9
Sorting 320ff. 1167ff.
Sorting bubble sort 1168
Sorting bubble sort cautioned against 321
Sorting by packing 1171
Sorting by reshaping array slices 1168
Sorting compared to selection 333
Sorting covariance matrix 669 681 1289
Sorting eigenvectors 46If. 1227
Sorting Heapsort 320 327f. 336 1171f. 1179
Sorting index table 320 329f. 1170 1173ff. 1176
Sorting operation count 320ff.
Sorting parallel algorithms 1168 1171f. 1176
Sorting Quicksort 320 323ff. 330 333 1169f.
Sorting radix sort 1172
Sorting rank table 320 332 1176
Sorting ranking 329 1176
Sorting Shell’s method 321ff. 1168
Sorting straight insertion 321f. 461f. 1167 1227
SP, defined 937
SPARC or SPARCstation 1/xxii 2/xix 4
SPARCstation 1/xxii 2/xix 4
Sparse linear equations 23 63ff. 732 1030
Sparse linear equations band diagonal 43 1019ff.
Sparse linear equations biconjugate gradient method 77 599 1034
Sparse linear equations data type for 1030
Sparse linear equations in inverse problems 804
Sparse linear equations indexed storage 71f. 1030
Sparse linear equations minimum residual method 78
Sparse linear equations named patterns 64 822
Sparse linear equations partial differential equations 822ff.
Sparse linear equations relaxation method for boundary value problems 754 1316
Sparse linear equations row-indexed storage 71f. 1030
Sparse linear equations wavelet transform 584 598
Spearman rank-order coefficient 634f. 694f. 1277
Special functions see “Function”
Spectral analysis see “Fourier transform”; “Periodogram”
Spectral density 541
Spectral density and data windowing 545ff.
Spectral density figures of merit for data windows 548f.
Spectral density normalization conventions 542f.
Spectral density one-sided PSD 492
Spectral density periodogram 543ff. 566 1258ff.
Spectral density power spectral density (PSD) 492f.
Spectral density power spectral density per unit time 493
Spectral density power spectrum estimation by FFT 542ff. 1254ff.
Spectral density power spectrum estimation by MEM 565ff. 1258
Spectral density two-sided PSD 493
Spectral density variance reduction in spectral estimation 545
Spectral lines, how to smooth 644
Spectral methods for partial differential equations 825
Spectral radius 856ff. 862
Spectral test for random number generator 274
Spectrum see “Fourier transform”
Spherical Bessel functions 234
Spherical Bessel functions routine for 245 1121
Spherical harmonics 246ff.
Spherical harmonics orthogonality 246
Spherical harmonics routine for 247f. 1122
Spherical harmonics stable recurrence for 247
Spherical harmonics table of 246 (see also “Associated Legendre polynomials”)
Spheroidal harmonics 764ff. 770ff. 1319ff.
Spheroidal harmonics boundary conditions 765
Spheroidal harmonics normalization 765
Spheroidal harmonics routine for 768ff. 1319ff. 1323ff.
SPLINE 100
Spline cubic 107ff. 1044f.
Spline gives tridiagonal system 109
Spline natural 109 1044f.
Spline operation count 109
Spline two-dimensional (bicubic) 120f. 1050f.
Spread matrix 808
Spread Spectrum 290
spread() intrinsic function 945 950 969 1000 1094 1290f.
spread() intrinsic function and dimensional expansion 966ff.
Square root, complex 172
Square root, multiple precision 912 1356f.
Square window 546 1254ff.
SSP (small-scale parallel) machines 965ff. 972 974 984 1011 1016ff. 1021 1059f. 1226ff. 1250
Stability 20f.
Stability and stiff differential equations 728f.
Stability Courant condition 829 832ff. 836 846
Stability diffusion equation 840
Stability in quadrature solution of Volterra equation 787f.
Stability mesh-drift in PDEs 834f.
Stability nonlinear 831 837
Stability of Clenshaw’s recurrence 177
Stability of Gauss — Jordan elimination 27 29
Stability of implicit differencing 729 840
Stability of polynomial deflation 363
Stability of recurrence relations 173ff. 177 224f. 227f. 232 247
Stability partial differential equations 820 827f.
Stability von Neumann analysis for PDEs 827f. 830 833f. 840
Stabilized Kolmogorov — Smirnov test 621
Stabilizing functional 798
Staggered leapfrog method 833f.
Standard (probable) errors 1288 1290
Standard deviation of a distribution 605 1269
Standard deviation of Fisher’s z 632
Standard deviation of linear correlation coefficient 630
Standard deviation of standard (probable) errors 610 656 661 667 671 684
Standard deviation of sum squared difference of ranks 635 1277
Stars, as text separator 1009
Statement function, superseded by internal subprogram 1057 1256
Statement labels 9
Statistical error 653
Statistical tests 603ff. 1269ff.
Statistical tests Anderson — Darling 621
Statistical tests average deviation 605 1269
Statistical tests bootstrap method 686f.
| Statistical tests chi-square 614f. 623ff. 1272 1275f.
Statistical tests contingency coefficient C 625 1275
Statistical tests contingency tables 622ff. 638 1275f.
Statistical tests correlation 603f.
Statistical tests Cramer’s V 625 1275
Statistical tests difference of distributions 614ff. 1272
Statistical tests difference of means 609ff. 1269f.
Statistical tests difference of variances 611 613 1271
Statistical tests entropy measures of association 626ff. 1275f.
Statistical tests F-test 611 613 1271
Statistical tests Fisher’s z-transformation 631f. 1276
Statistical tests for periodic signal 570
Statistical tests for shift vs. for spread 620f.
Statistical tests general paradigm 603
Statistical tests Kendall’s tau 634 637ff. 1279
Statistical tests Kolmogorov — Smirnov 614 617ff. 640 694 1273f. 1281
Statistical tests Kuiper’s statistic 621
Statistical tests kurtosis 606 608 1269
Statistical tests L-estimates 694
Statistical tests linear correlation coefficient 630ff. 1276
Statistical tests M-estimates 694ff.
Statistical tests mean 603ff. 608ff. 1269f.
Statistical tests measures of association 604 622ff. 1275
Statistical tests measures of central tendency 604ff. 1269
Statistical tests median 605 694
Statistical tests mode 605
Statistical tests moments 604ff. 608 1269
Statistical tests nonparametric correlation 633ff. 1277
Statistical tests Pearson’s r 630ff. 1276
Statistical tests phi statistic 625
Statistical tests R-estimates 694
Statistical tests rank correlation 633ff. 1277
Statistical tests robust 605 634 694ff.
Statistical tests semi-invariants 608
Statistical tests significance 609f. 1269ff.
Statistical tests significance, one- vs. two-sided 613 632
Statistical tests skewness 606 608 1269
Statistical tests Spearman rank-order coefficient 634f. 694f. 1277
Statistical tests standard deviation 605 1269
Statistical tests strength vs. significance 609f. 622
Statistical tests Student’s t 610 631 1269
Statistical tests Student’s t, for correlation 631
Statistical tests Student’s t, paired samples 612 1271
Statistical tests Student’s t, Spearman rank-order coefficient 634 1277
Statistical tests Student’s t, unequal variances 611 1270
Statistical tests sum squared difference of ranks 635 1277
Statistical tests Tukey’s trimean 694
Statistical tests two-dimensional 640 1281ff.
Statistical tests variance 603ff. 607f. 612f. 1269ff.
Statistical tests Wilcoxon 694 (see also “Error”; “Robust estimation”)
Steak, without sizzle 809
Steed’s method Bessel functions 234 239
Steed’s method continued fractions 164f.
Steepest descent method 414
Steepest descent method in inverse problems 804
Step doubling 130 708f. 1052
Step tripling 136 1055
Stieltjes, procedure of 151
Stiff equations 703 727ff. 1308ff.
Stiff equations, Kaps — Rentrop method 730 1308
Stiff equations, methods compared 739
Stiff equations, predictor — corrector method 730
Stiff equations, r.h.s. independent of x 729f.
Stiff equations, Rosenbrock method 730 1308
Stiff equations, scaling of variables 730
Stiff equations, semi — implicit midpoint rule 735f. 1310f.
Stiff equations, semi-implicit extrapolation method 730 1310f.
Stiff functions 100 399
Stirling’s approximation 206 812
Stoermer’s rule 726 1307
Stopping criterion, in multigrid method 875f.
Stopping criterion, in polynomial root finding 366
Storage association 2/xiv
Storage band diagonal matrix 44 1019
Storage sparse matrices 71f. 1030
Straight injection 867
Straight insertion 321f. 461f. 1167 1227
Straight line fitting 655ff. 667f. 1285ff.
Straight line fitting errors in both coordinates 660ff. 1286ff.
Straight line fitting robust estimation 698 1294ff.
Strassen’s fast matrix algorithms 96f.
Stratified sampling, Monte Carlo 308f. 314
Stride (of an array) 944
Stride (of an array)communication bottleneck 969
Strongly implicit procedure (SIPSOL) 824
Structure constructor 2/xii
Structured programming 5ff.
Student’s probability distribution 221f.
Student’s t-test for correlation 631
Student’s t-test for difference of means 610 1269
Student’s t-test for difference of means (paired samples) 612 1271
Student’s t-test for difference of means (unequal variances) 611 1270
Student’s t-test for difference of ranks 635 1277
Student’s t-test for difference of ranks, Spearman rank-order coefficient 634 1277
Sturmian sequence 469
Sub-random sequences see “Quasi-random sequence”
Subprogram 938
Subprogram for data hiding 957 1209 1293 1296
Subprogram in module 940
Subprogram internal 954 957 1057 1067 1226 1256
Subprogram undefined variables on exit 952f. 961 1070 1266 1293 1302
Subscript triplet (for array) 944
Subtraction, multiple precision 907 1353
Subtractive method for random number generator 273 1143
Subvector scaling 972 974 996 1000
Successive over-relaxation (SOR) 857ff. 862 1332f.
Successive over-relaxation bad in multigrid method 866
Successive over-relaxation Chebyshev acceleration 859f. 1332f.
Successive over-relaxation choice of overrelaxation parameter 858
Successive over-relaxation parallelization 1333
Successive over-relaxation with logical mask 1333f.
Sum squared difference of ranks 634 1277
sum() intrinsic function 945 948 966
Sums see “Series”
Sun 1/xxii 2/xix 886
Supernova 1987A 640
SVD see “Singular value decomposition (SVD)”
swap() utility function 987 990f. 1015 1210
Symbol, of operator 866f.
Synthetic division 84 167 362 370
Synthetic division parallel algorithms 977ff. 999 1048 1071f. 1079 1192
Synthetic division repeated 97 8f.
Systematic errors 653
T ableau (interpolation) 103 183
Tangent function, continued fraction 163
Target, for pointer 938f. 945 952f.
Taylor series 180 355f. 408 702 709 742 754 759
Test programs 3
Thermodynamics, analogy for simulated annealing 437
Thinking Machines, Inc. 964
Threshold multiply of sparse matrices 74 1031
Tides 560f.
Tikhonov — Miller regularization 799ff.
Time domain 490
Time splitting 847f. 861
tiny() intrinsic function 952
Toeplitz matrix 82 85ff 195 1038
Toeplitz matrix LU decomposition 87
Toeplitz matrix new, fast algorithms 88f.
Toeplitz matrix nonsymmetric 86ff. 1038
Tongue twisters 333
Torus 297f. 304
Trade — off curve 795 809
Trademarks 1/xxii 2/xixf.
Transformation Gauss 256
Transformation Landen 256
Transformation method for random number generator 277ff.
Transformational functions 948ff.
Transforms, number theoretic 503f.
Transport error 831ff.
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