978 Index multidimensional 107f.,123ff. for linear algebraic equations 35 in multigrid method 876 required for two-point boundary value Neville's algorithm 108f.,188 problems 753 Nystrom 792 in root finding 347f. offset arrays 110,119 Iteration matrix 865 operation count for 106 ITPACK 78 operator 873 ivector()utility 943 order of 106 and ordinary differential equations 107 oscillations of polynomial 106,120,396. Jacobi matrix,for Gaussian quadrature 156 406 Jacobi transformation (or rotation)100,460, parabolic,for minimum finding 402 463fE,469,481,495 polynomial 105,108ff.,188 Jacobian determinant 288f.,783 rational Chebyshev approximation 204ff. Jacobian elliptic functions 261,269f. rational function 105,111ff.,200ff.,231f., Jacobian matrix 381,383,386,389,738 724f,731 singular in Newton's rule 393 reverse (extirpolation)581f. Jacobi's method (relaxation)864f,866,873 spline 106,113ff.,127f. Jenkins-Traub method 376 trigonometric 105 Julian Day 1,12,14 see also Fitting Jump transposition errors 902 Interval variable (statistics)628 Intrinsic correlation function (ICF)model 826 Inverse hyperbolic function 184.262 K-S test see Kolmogorov-Smimov test Inverse iteration see Eigensystems Kalman filter 705 Inverse problems 789,804ff. Kaps-Rentrop method 737 Backus-Gilbert method 815ff. Kendall's tau 640,642ff. Bayesian approach 808,820,825f. Kermit checksum 897 central idea 808 Kernel 788f constrained linear inversion method 808ff. averaging,in Backus-Gilbert method 816f. data inversion 816 degenerate 794 deterministic constraints 813ff. finite rank 794 inverse response 816f in geophysics 818 Gerchberg-Saxton algorithm 814f. separable 794 incomplete Fourier coefficients 822 singular 797f. and integral equations 789 symmetric 793f. Kernighan Ritchie C(K&R C)2,16,24, linear regularization 808ff. 90 maximum entropy method(MEM)818ff., 824f. Keys used in sorting 338,897 MEM demystified 823 Kolmogorov-Smirnov test 620,623ff.,699 Phillips-Twomey method 808ff two-dimensional 645ff. variants 626ff..645ff. principal solution 806 Kuiper's statistic 627 regularization 805ff. Kurtosis 612.614 regularizing operator 807 stabilizing functional 807 Tikhonov-Miller regularization 808ff. L-estimate 699 trade-off curve 804 Labels,statement 8 trade-off curve,Backus-Gilbert method Lag498.545f,560 818 Lagrange multiplier 804 two-dimensional regularization 812 Lagrange's formula for polynomial interpola- use of conjugate gradient minimization tion91.108.582,585 812f,824 Laguerre's method 348,371ff. use of convex sets 813f. Lanczos lemma 504f. use of Fourier transform 812,814 Lanczos method for gamma function 213 Van Cittert's method 813 Landen transformation 262 Inverse quadratic interpolation 360,402年 LAPACK 35 Inverse response kemel,in Backus-Gilbert Laplace's equation 252,827 method 816f. see also Poisson equation Inverse trigonometric function 262 Las Vegas 631 ISBN (International Standard Book Number) Latin square or hypercube 315 checksum 901 Laurent series 573 Iterated integrals 161 Lax method 837ff.,845,854f Iteration 8 multidimensional 854f. functional 748 Lax-Wendroff method 844ff. to improve solution of linear algebraic Leakage in power spectrum estimation 551, equations 55ff.,201 554f978 Index multidimensional 107f., 123ff. in multigrid method 876 Neville’s algorithm 108f., 188 Nystrom 792 offset arrays 110, 119 operation count for 106 operator 873 order of 106 and ordinary differential equations 107 oscillations of polynomial 106, 120, 396, 406 parabolic, for minimum finding 402 polynomial 105, 108ff., 188 rational Chebyshev approximation 204ff. rational function 105, 111ff., 200ff., 231f., 724ff., 731 reverse (extirpolation) 581f. spline 106, 113ff., 127f. trigonometric 105 see also Fitting Interval variable (statistics) 628 Intrinsic correlation function (ICF) model 826 Inverse hyperbolic function 184, 262 Inverse iteration see Eigensystems Inverse problems 789, 804ff. Backus-Gilbert method 815ff. Bayesian approach 808, 820, 825f. central idea 808 constrained linear inversion method 808ff. data inversion 816 deterministic constraints 813ff. in geophysics 818 Gerchberg-Saxton algorithm 814f. incomplete Fourier coefficients 822 and integral equations 789 linear regularization 808ff. maximum entropy method (MEM) 818ff., 824f. MEM demystified 823 Phillips-Twomey method 808ff. principal solution 806 regularization 805ff. regularizing operator 807 stabilizing functional 807 Tikhonov-Miller regularization 808ff. trade-off curve 804 trade-off curve, Backus-Gilbert method 818 two-dimensional regularization 812 use of conjugate gradient minimization 812f., 824 use of convex sets 813f. use of Fourier transform 812, 814 Van Cittert’s method 813 Inverse quadratic interpolation 360, 402ff. Inverse response kernel, in Backus-Gilbert method 816f. Inverse trigonometric function 262 ISBN (International Standard Book Number) checksum 901 Iterated integrals 161 Iteration 8 functional 748 to improve solution of linear algebraic equations 55ff., 201 for linear algebraic equations 35 required for two-point boundary value problems 753 in root finding 347f. Iteration matrix 865 ITPACK 78 ivector() utility 943 Jacobi matrix, for Gaussian quadrature 156 Jacobi transformation (or rotation) 100, 460, 463ff., 469, 481, 495 Jacobian determinant 288f., 783 Jacobian elliptic functions 261, 269f. Jacobian matrix 381, 383, 386, 389, 738 singular in Newton’s rule 393 Jacobi’s method (relaxation) 864f., 866, 873 Jenkins-Traub method 376 Julian Day 1, 12, 14 Jump transposition errors 902 K-S test see Kolmogorov-Smirnov test Kalman filter 705 Kaps-Rentrop method 737 Kendall’s tau 640, 642ff. Kermit checksum 897 Kernel 788f. averaging, in Backus-Gilbert method 816f. degenerate 794 finite rank 794 inverse response 816f. separable 794 singular 797f. symmetric 793f. Kernighan & Ritchie C (K&R C) 2, 16, 24, 930 Keys used in sorting 338, 897 Kolmogorov-Smirnov test 620, 623ff., 699 two-dimensional 645ff. variants 626ff., 645ff. Kuiper’s statistic 627 Kurtosis 612, 614 L-estimate 699 Labels, statement 8 Lag 498, 545f., 560 Lagrange multiplier 804 Lagrange’s formula for polynomial interpola￾tion 91, 108, 582, 585 Laguerre’s method 348, 371ff. Lanczos lemma 504f. Lanczos method for gamma function 213 Landen transformation 262 LAPACK 35 Laplace’s equation 252, 827 see also Poisson equation Las Vegas 631 Latin square or hypercube 315 Laurent series 573 Lax method 837ff., 845, 854f. multidimensional 854f. Lax-Wendroff method 844ff. Leakage in power spectrum estimation 551, 554f