974 Index Finite difference equations(FDEs)762,772, standard (probable)errors on fitted parame- 783 ters663,667E,673,677.689ǖ alternating-direction implicit method (ADI) straight line 661ff.,673f,703 856.870f. straight line,errors in both coordinates art,not science 838 666正 Cayley's form for unitary operator 853 see also Error,Least squares fitting;Max- Courant condition 838,841,845 imum likelihood estimate;Robust esti- Courant condition (multidimensional)855 mation Crank-Nicolson method 848.853.855 Five-point difference star 876 eigenmodes of 836f. Fixed point format 28 explicit vs.implicit schemes 836 Fletcher-Powell algorithm see Davidon-Fletcher- forward Euler 835f. Powell algorithm Forward Time Centered Space (FTCS) Fletcher-Reeves algorithm 396f.,421ff. 836f,847f,852,864 float to double conversion 24f. implicit scheme 848 Floating point co-processor 894 Lax method 837ff..845 Floating point format 28,890 Lax method (multidimensional)854f. care in numerical derivatives 186 mesh drifting instability 843f IEEE 285.890f. numerical derivatives 186 Flux-conservative initial value problems 834ff. partial differential equations 830ff. FMG (full multigrid method)872,877f. in relaxation methods 762ff for iteration 8,11 staggered leapfrog method 842f Formats of numbers 28,890 two-step Lax-Wendroff method 844ff FORTRAN 16.20 upwind differencing 841f..846 Numerical Recipes in xv,I see also Partial differential equations Forward deflation 370 Finite element methods,partial differential Forward difference operator 167 equations 833f. Forward Euler differencing 835f Finite impulse response (FIR)538 Forward Time Centered Space see FTCS Finkelstein,S.xii Fourier analysis and cyclic reduction (FACR) FIR (finite impulse response)filter 559f. 858,863 Fisher's z-transformation 637f. Fourier and spectral applications 537ff Fitting 656ff. Fourier integrals basis functions 671 attenuation factors 590 by Chebyshev approximation 191f. endpoint corrections 585f. chi-square 659ff. tail integration by parts 591 confidence levels related to chi-square val- use of fast Fourier transform (FFT)584ff. ues 696ff. Fourier transform 105,496ff confidence levels from singular value de aliasing 501,576 composition (SVD)698 approximation of Dawson's integral 259 confidence limits on fitted parameters 689ff. autocorrelation 498 covariance matrix not always meaningful basis functions compared 514f. 657,695 contrasted with wavelet transform 591f., degeneracy of parameters 679 601 an exponential 679 convolution 498.509.538ff.,918 freezing parameters in 674,705 correlation 498.545f. Gaussians,a sum of 687f. cosine transform 196,517E,860f general linear least squares 671ff. cosine transform,second form 519,861 Kalman filter 705 critical sampling 500,550,552 K-S test,caution regarding 627 definition 496 least squares 657ff. discrete Fourier transform (DFT)190, Legendre polynomials 680 500ff. Levenberg-Marquardt method 683ff.,825 Gaussian function 607 linear regression 661ff. image processing 812,814 maximum likelihood estimation 658, infinite range 590f. 699f inverse of discrete Fourier transform 503 Monte Carlo simulation 627,660,689ff. method for partial differential equations multidimensional 680 857E nonlinear models 681ff missing data 576 nonlinear models,advanced methods 688 missing data,fast algorithm 581f. nonlinear problems that are linear 679 Nyquist frequency 500ff,526,550,552, nonnormal errors 662,695,699ff. 576.579 polynomial90,120,197,650f,671,679f optimal(Wiener)filtering 547ff,565f. by rational Chebyshey approximation 204ff Parseval's theorem 498,504,551 robust methods 699ff. power spectral density (PSD)498f. of sharp spectral features 573 power spectrum estimation by FFT 549ff.974 Index Finite difference equations (FDEs) 762, 772, 783 alternating-direction implicit method (ADI) 856, 870f. art, not science 838 Cayley’s form for unitary operator 853 Courant condition 838, 841, 845 Courant condition (multidimensional) 855 Crank-Nicolson method 848, 853, 855 eigenmodes of 836f. explicit vs. implicit schemes 836 forward Euler 835f. Forward Time Centered Space (FTCS) 836ff., 847ff., 852, 864 implicit scheme 848 Lax method 837ff., 845 Lax method (multidimensional) 854f. mesh drifting instability 843f. numerical derivatives 186 partial differential equations 830ff. in relaxation methods 762ff. staggered leapfrog method 842f. two-step Lax-Wendroff method 844ff. upwind differencing 841f., 846 see also Partial differential equations Finite element methods, partial differential equations 833f. Finite impulse response (FIR) 538 Finkelstein, S. xii FIR (finite impulse response) filter 559f. Fisher’s z-transformation 637f. Fitting 656ff. basis functions 671 by Chebyshev approximation 191f. chi-square 659ff. confidence levels related to chi-square val￾ues 696ff. confidence levels from singular value de￾composition (SVD) 698 confidence limits on fitted parameters 689ff. covariance matrix not always meaningful 657, 695 degeneracy of parameters 679 an exponential 679 freezing parameters in 674, 705 Gaussians, a sum of 687f. general linear least squares 671ff. Kalman filter 705 K–S test, caution regarding 627 least squares 657ff. Legendre polynomials 680 Levenberg-Marquardt method 683ff., 825 linear regression 661ff. maximum likelihood estimation 658, 699ff. Monte Carlo simulation 627, 660, 689ff. multidimensional 680 nonlinear models 681ff. nonlinear models, advanced methods 688 nonlinear problems that are linear 679 nonnormal errors 662, 695, 699ff. polynomial 90, 120, 197, 650f., 671, 679f. by rational Chebyshev approximation 204ff. robust methods 699ff. of sharp spectral features 573 standard (probable) errors on fitted parame￾ters 663, 667f., 673, 677, 689ff. straight line 661ff., 673f., 703 straight line, errors in both coordinates 666ff. see also Error; Least squares fitting; Max￾imum likelihood estimate; Robust esti￾mation Five-point difference star 876 Fixed point format 28 Fletcher-Powell algorithm see Davidon-Fletcher￾Powell algorithm Fletcher-Reeves algorithm 396f., 421ff. float to double conversion 24f. Floating point co-processor 894 Floating point format 28, 890 care in numerical derivatives 186 IEEE 285, 890f. Flux-conservative initial value problems 834ff. FMG (full multigrid method) 872, 877f. for iteration 8, 11 Formats of numbers 28, 890 FORTRAN 16, 20 Numerical Recipes in xv, 1 Forward deflation 370 Forward difference operator 167 Forward Euler differencing 835f. Forward Time Centered Space see FTCS Fourier analysis and cyclic reduction (FACR) 858, 863 Fourier and spectral applications 537ff. Fourier integrals attenuation factors 590 endpoint corrections 585f. tail integration by parts 591 use of fast Fourier transform (FFT) 584ff. Fourier transform 105, 496ff. aliasing 501, 576 approximation of Dawson’s integral 259 autocorrelation 498 basis functions compared 514f. contrasted with wavelet transform 591f., 601 convolution 498, 509, 538ff., 918 correlation 498, 545f. cosine transform 196, 517ff., 860f. cosine transform, second form 519, 861 critical sampling 500, 550, 552 definition 496 discrete Fourier transform (DFT) 190, 500ff. Gaussian function 607 image processing 812, 814 infinite range 590f. inverse of discrete Fourier transform 503 method for partial differential equations 857ff. missing data 576 missing data, fast algorithm 581f. Nyquist frequency 500ff., 526, 550, 552, 576, 579 optimal (Wiener) filtering 547ff., 565f. Parseval’s theorem 498, 504, 551 power spectral density (PSD) 498f. power spectrum estimation by FFT 549ff