c21-2 (779630), страница 8
Текст из файла (страница 8)
xiiSobol’s quasi-random sequence 311Sonata 8Sonnet 8Sorting 329ff.bubble sort cautioned against 330compared to selection 341covariance matrix 675, 687eigenvectors 468f.Heapsort 329, 336f., 344index table 329, 338operation count 329ff.Quicksort 329, 332ff., 338, 341rank table 329, 340f.ranking 338Shell’s method 330ff.straight insertion 330f., 468SPARC or SPARCstation xvii, 3Sparse linear equations 33, 71ff., 739band diagonal 51ff.biconjugate gradient method 84f., 606indexed storage 78f.in inverse problems 813minimum residual method 85named patterns 71, 831partial differential equations 831ff.991relaxation method for boundary value problems 762row-indexed storage 78f.wavelet transform 591, 606see also MatrixSpearman rank-order coefficient 640f., 699f.Special functions see FunctionSpectral analysis see Fourier transform; PeriodogramSpectral density 548and data windowing 553ff.figures of merit for data windows 554f.normalization conventions 550one-sided PSD 498periodogram 550ff., 574power spectral density (PSD) 498f.power spectral density per unit time 499power spectrum estimation by FFT 549ff.power spectrum estimation by MEM 572ff.two-sided PSD 499variance reduction in spectral estimation552Spectral lines, how to smooth 650Spectral methods for partial differential equations 833f.Spectral radius 865ff., 871Spectral test for random number generator284Spectrum see Fourier transformSpherical Bessel functions 240routine for 251Spherical harmonics 252f.orthogonality 252routine for 254stable recurrence for 253table of 253see also Associated Legendre polynomialsSpheroidal harmonics 772ff., 779f., 781boundary conditions 774normalization 774routine for 777ff., 780f., 781f.Spline 106cubic 113ff.gives tridiagonal system 115natural 115operation count 115two-dimensional (bicubic) 127f.Spread matrix 817Spread spectrum 300Square root, complex 177f.Square root, multiple precision 921Square window 553Squaring, macro in C 27Stability 30f.of Clenshaw’s recurrence 182f.Courant condition 838, 841ff., 845, 855diffusion equation 849of Gauss-Jordan elimination 36, 38of implicit differencing 735f., 849mesh-drift in PDEs 843f.nonlinear 840, 846partial differential equations 829, 836f.of polynomial deflation 370in quadrature solution of Volterra equation796992of recurrence relations 179ff., 182f., 231,239, 253and stiff differential equations 735f.von Neumann analysis for PDEs 836f.,839, 842, 849see also AccuracyStabilized Kolmogorov-Smirnov test 626f.Stabilizing functional 807Staggered leapfrog method 842f.Standard deviationof a distribution 611of Fisher’s z 637of linear correlation coefficient 636of sum squared difference of ranks 641Standard (probable) errors 616, 662, 667,673, 677, 689Statement labels 8Statistical error 659Statistical tests 609ff.Anderson-Darling 626f.average deviation 611bootstrap method 691f.chi-square 620f., 630ff.contingency coefficient C 631contingency tables 628ff., 644correlation 609f.Cramer’s V 631difference of distributions 620ff.difference of means 615ff.difference of variances 617, 619entropy measures of association 632ff.F-test 617, 619Fisher’s z-transformation 637f.general paradigm 609Kendall’s tau 640, 642ff.Kolmogorov-Smirnov 620, 623ff., 645ff.,699Kuiper’s statistic 627kurtosis 612, 614L-estimates 699linear correlation coefficient 636ff.M-estimates 699ff.mean 609ff., 614, 615ff.measures of association 610, 628ff.measures of central tendency 610ff.median 611, 699mode 611moments 610ff., 614nonparametric correlation 639ff.Pearson’s r 636ff.for periodic signal 577f.phi statistic 631R-estimates 699f.rank correlation 639ff.robust 611, 640, 699ff.semi-invariants 614for shift vs.
for spread 626f.significance 615f.significance, one- vs. two-sided 619, 638skewness 612, 614Spearman rank-order coefficient 640f.,699f.standard deviation 611strength vs. significance 615, 628Student’s t 616, 637IndexStudent’s t, for correlation 637Student’s t, paired samples 618Student’s t, Spearman rank-order coefficient 640Student’s t, unequal variances 617sum squared difference of ranks 640f.Tukey’s trimean 699two-dimensional 645ff.variance 609ff., 613, 618Wilcoxon 699see also Error; Robust estimation__STDC__ macro 17, 930Steak, without sizzle 818Steed’s methodBessel functions 240ff., 246continued fractions 170f.Steepest descent method 421in inverse problems 813Stepdoubling 136, 715tripling 143Stieltjes, procedure of 157Stiff equations 709, 734ff.Kaps-Rentrop method 737methods compared 747predictor-corrector method 737r.h.s.
independent of x 736Rosenbrock method 737ff.scaling of variables 737semi-implicit extrapolation method 737semi-implicit midpoint rule 743Stiff functions 106, 406Stirling’s approximation 213, 821Stoermer’s rule 732f.Stopping criterion, in multigrid method 884Stopping criterion, in polynomial root finding373Storageband diagonal matrix 52scheme for matrix in C 20f., 33f., 940f.sparse matrices 78f.Straight injection 876Straight insertion 330f., 468Straight line fitting 661ff., 673f.errors in both coordinates 666ff.robust estimation 703Strassen’s fast matrix algorithms 102ff.Stratified sampling, Monte Carlo 317f., 323Strongly implicit procedure (SIPSOL) 833Structured programming 5ff.Student’s probability distribution 226, 228Student’s t-testfor correlation 637for difference of ranks 641for difference of means 616for difference of means (paired samples)618for difference of means (unequal variances)617Spearman rank-order coefficient 640Sturmian sequence 475f.submatrix() utility 945Submatrixcaution on freeing 23of existing matrix 22, 945IndexSub-random sequences see Quasi-random sequenceSubtraction, multiple precision 916Subtractive method for random number generator 282Successive over-relaxation (SOR) 866ff., 871bad in multigrid method 875Chebyshev acceleration 868f.choice of overrelaxation parameter 866f.Sum squared difference of ranks 640Sums see SeriesSun xvii, 894SPARCstation xvii, 3Supernova 1987A 645SVD see Singular value decomposition (SVD)switch structure 14Symbol, of operator 875f.Synthetic division 91, 174, 369, 377Systematic errors 659T ableau (interpolation)109, 189Tangent function, continued fraction 169Taylor series 186, 362, 414, 708, 715, 750,763, 767Test programs 3TEX xiiiThermodynamics, analogy for simulated annealing 444f.Threshold multiply of sparse matrices 81ff.Tides 568Tikhonov-Miller regularization 808ff.Time domain 496Time splitting 856f., 870Toeplitz matrix 90, 92ff., 201LU decomposition 94new, fast algorithms 95f.nonsymmetric 93ff.Tongue twisters 341Torus 305ff., 313ff.Trade-off curve 804, 818Trademarks xviiTransformationGauss 262Landen 262method for random number generator 287ff.Transforms, number theoretic 509f.Transport error 840Transpose of sparse matrix 80f.Trapezoidal rule 131, 133, 136ff., 140, 586,590, 791f., 795Traveling salesman problem 445ff.Tridiagonal matrix 50f., 66, 156, 460f., 494in alternating-direction implicit method(ADI) 870f.from cubic spline 115cyclic 74f.in cyclic reduction 862eigenvalues 475ff.with fringes 831from operator splitting 870f.reduction of symmetric matrix to 469ff.,476see also Matrix993Trigonometricfunctions, linear sequences 178f.functions, recurrence relation 178, 579functions, tan(θ/2) as minimal 179interpolation 105solution of cubic equation 184f.Truncation error 30, 406, 715, 889f.in multigrid method 883in numerical derivatives 186Tukey’s biweight 702Tukey’s trimean 699Turbo Pascal (Borland) 7Twin errors 902Two-dimensional see MultidimensionalTwo-dimensional K–S test 645ff.Two-pass algorithm for variance 613Two-point boundary value problems 708,753ff.automated allocation of mesh points 783f.,786boundary conditions 753ff., 757, 760,779f.difficult cases 760eigenvalue problem for differential equations 756, 772ff., 779, 781free boundary problem 756, 785grid (mesh) points 754f., 762, 783f., 786internal boundary conditions 784ff.internal singular points 784ff.linear requires no iteration 759multiple shooting 762problems reducible to standard form 756regularity condition 784relaxation method 754f., 762ff.relaxation method, example of 772ff.shooting to a fitting point 760ff.shooting method 754, 757ff., 779f., 781shooting method, example of 779f., 781singular endpoints 760, 773, 780see also Elliptic partial differential equationsTwo-sided exponential error distribution 701Two-sided power spectral density 499Two-step Lax-Wendroff method 844ff.U LTRIX xvii, 3Uncertainty coefficient 634Uncertainty principle 607Underflow, in IEEE arithmetic 891Underrelaxation 866Uniform deviates see Random deviates, uniformUnit-offset array 18, 940f.Unitary (function) 852f.Unitary (matrix) see MatrixUNIX xii, xvii, 3, 16, 285, 303, 894Upper Hessenberg matrix see Hessenberg matrixUpwind differencing 841f., 846U.S.
Postal Service barcode 902Utility functionscomplex.c 23f., 948ff.nrutil.c 2, 19, 21f., 940, 942ff.994V -cycle874Validation of Numerical Recipes procedures2f.Valley, long or narrow 410, 413, 416Van Cittert’s method 813Van Wijngaarden-Dekker-Brent method seeBrent’s methodVandermonde matrix 90ff., 120Variable length code 903Variable metric method 397, 425ff.compared to conjugate gradient method425f.Variable step-size integration 129, 141, 709,713, 725ff., 733f., 738, 744, 749f.Variance(s)of distribution 609ff., 614, 617, 619pooled 616reduction of (in Monte Carlo) 308, 316ff.statistical differences between two 615two-pass algorithm for computing 613see also CovarianceVariational methods, partial differential equations 833VAX xvii, 285, 303Vector see ArrayVectors, representation in C 18vector() utility 943VEGAS algorithm for Monte Carlo 319ff.Verhoeff’s algorithm for checksums 902Viète’s formulas for cubic roots 184f.Virus, computer 897Viscosityartificial 840, 846numerical 839, 840, 846VMS xviivoid (parameter type list) 17Volterra equations 789f.adaptive stepsize control 797analogy with ODEs 794f.block-by-block method 797first kind 790, 795nonlinear 790, 796second kind 790, 794f.unstable quadrature 796von Neumann-Richtmyer artificial viscosity846von Neumann stability analysis for PDEs 836f.,839, 842, 849Vowellish (coding example) 904f., 910W -cycle874Warranty, disclaimer of xviWave equation 252, 827, 834f.Wavelet transform 591ff.appearance of wavelets 598f.approximation condition of order p 592f.coefficient values 594, 596contrasted with Fourier transform 591f.,601Daubechies wavelet filter coefficients 592ff.,596, 598, 601, 605detail information 593discrete wavelet transform (DWT) 594f.DWT (discrete wavelet transform) 594f.Indexeliminating wrap-around 594f.fast solution of linear equations 603ff.filters 599f.and Fourier domain 599f.image processing 603for integral equations 791inverse 594Lemarie’s wavelet 600of linear operator 603ff.mother-function coefficient 594mother functions 591multidimensional 602nonsmoothness of wavelets 598f.pyramidal algorithm 594quadrature mirror filter 592smooth information 593truncation 601f.wavelet filter coefficient 592, 594wavelets 591, 598ff.Wavelets see Wavelet transformWeber function 210Weighted Kolmogorov-Smirnov test 626f.Weighted least-squares fitting see Least squaresfittingWeighting, full vs.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
