Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in FORTRAN77 :: Электронная библиотека попечительского совета мехмата МГУ

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Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in FORTRAN77

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Название: Numerical recipes in FORTRAN77

Авторы: Press W.H., Teukolsky S.A., Vetterling W.T.

Язык:

Рубрика: Математика/Численные методы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1992

Количество страниц: 973

Добавлена в каталог: 01.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Sine function evaluated from tan $(\theta/2)$       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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