Index 969 Conventions in C programs 25ff. routine for 258f Convergence series 257 accelerated,for series 166ff Cosine transform see Fast Fourier transform of algorithm forπ915 (FFT);Fourier transform criteria for353,398f,410,489f.,495 Coulomb wave function 210,240 684f,767 Courant condition 838,841,843,845 eigenvalues accelerated by shifting 477f multidimensional 855 golden ratio 354,406 Courant-Friedrichs-Lewy stability criterion see of golden section search 398f. Courant condition of Levenberg-Marquardt method 684f Covariance linear 353,400 a priori 705 of QL method 477f. in general linear least squares 673,677 quadratic57,358,364f.,415f,427,915 matrix,by Cholesky decomposition 98, ate353,359f,364f. 673 recurrence relation 181 matrix,of errors 805,817 of Ridders'method 358 matrix,is inverse of Hessian matrix 685 series vs.continued fraction 169f. matrix,when it is meaningful 695f. and spectral radius 865ff.,871 in nonlinear models 685,687 convert_matrix()utility 945 relation to chi-square 695ff. Convex sets,use in inverse problems 813f. from singular value decomposition (SVD) Convolution 698 denoted by asterisk 498 in straight line fitting 663 finite impulse response(FIR)538 CR method see Cyclic reduction (CR) of functions 498.509 Cramer's V 631 of large data sets 543f. Crank-Nicolson method 848,853,855 for multiple precision arithmetic 918 CRC (cyclic redundancy check)896ff. multiplication as 918 CRC-12898 necessity for optimal filtering 542 CRC-16 polynomial 898 overlap-add method 544 CRC-CCITT 898 overlap-save method 543f. Creativity,essay on 8 and polynomial interpolation 120 Critical (Nyquist)sampling 500,550 relation to wavelet transform 1592 Cross(denotes matrix outer product)73 theorem 498,538ff.553 Crosstabulation analysis 629 theorem,discrete 538ff. see also Contingency table treatment of end effects 540 Crout's algorithm 44ff.,53 use of FFT 530,538ff. Cubic equations 183ff.,367 wraparound problem 540 Cubic spline interpolation 113ff. Cooley-Tukey FFT algorithm 509 see also Spline Co-processor,floating point 894 Cumulative binomial distribution 226,229 Copyright rules xvi Cumulative Poisson function 221 Cornwell-Evans algorithm 825 related to incomplete gamma function 221 Corporate promotion ladder 336f. Curvature matrix see Hessian matrix Corrected two-pass algorithm 613 cvector()utility 943 Correction,in multigrid method 872 Cycle,in multigrid method 874 Correlation coefficient (linear)636ff. Cyclic Jacobi method 466 Correlation function 498 Cyclic reduction (CR)857f.,861f. autocorrelation 498,546,565 Cyclic redundancy check(CRC)896ff. and Fourier transforms 498 Cyclic tridiagonal systems 74f. theorem 498.545 treatment of end effects 546 using FFT 545f. Danielson-Lanczos lemma 504f..532 Wiener-Khinchin theorem 498.574 Data Correlation,statistical 609f.,628 assigning keys to 897 Kendall's tau 640,642ff. continuous vs.binned 620 linear correlation coefficient 636ff.,664 entropy 632ff,903f. linear related to least square fitting 636 essay on 609 664 fitting 656ff. nonparametric or rank statistical 639ff. fraudulent 661 among parameters in a fit 663,673,676 glitches in 659 in random number generators 277 iid (independent and identically distributed) Spearman rank-order coefficient 640f. 691 sum squared difference of ranks 640 modeling 656ff. Cosine function,recurrence 178 serial port 899 Cosine integral 255,257ff. smoothing 610,650ff. continued fraction 257 statistical tests 609ff.Index 969 Conventions in C programs 25ff. Convergence accelerated, for series 166ff. of algorithm for π 915 criteria for 353, 398f., 410, 489f., 495, 684f., 767 eigenvalues accelerated by shifting 477f. golden ratio 354, 406 of golden section search 398f. of Levenberg-Marquardt method 684f. linear 353, 400 of QL method 477f. quadratic 57, 358, 364f., 415f., 427, 915 rate 353, 359f., 364f. recurrence relation 181 of Ridders’ method 358 series vs. continued fraction 169f. and spectral radius 865ff., 871 convert_matrix() utility 945 Convex sets, use in inverse problems 813f. Convolution denoted by asterisk 498 finite impulse response (FIR) 538 of functions 498, 509 of large data sets 543f. for multiple precision arithmetic 918 multiplication as 918 necessity for optimal filtering 542 overlap-add method 544 overlap-save method 543f. and polynomial interpolation 120 relation to wavelet transform 592 theorem 498, 538ff., 553 theorem, discrete 538ff. treatment of end effects 540 use of FFT 530, 538ff. wraparound problem 540 Cooley-Tukey FFT algorithm 509 Co-processor, floating point 894 Copyright rules xvi Cornwell-Evans algorithm 825 Corporate promotion ladder 336f. Corrected two-pass algorithm 613 Correction, in multigrid method 872 Correlation coefficient (linear) 636ff. Correlation function 498 autocorrelation 498, 546, 565 and Fourier transforms 498 theorem 498, 545 treatment of end effects 546 using FFT 545f. Wiener-Khinchin theorem 498, 574 Correlation, statistical 609f., 628 Kendall’s tau 640, 642ff. linear correlation coefficient 636ff., 664 linear related to least square fitting 636, 664 nonparametric or rank statistical 639ff. among parameters in a fit 663, 673, 676 in random number generators 277 Spearman rank-order coefficient 640f. sum squared difference of ranks 640 Cosine function, recurrence 178 Cosine integral 255, 257ff. continued fraction 257 routine for 258f. series 257 Cosine transform see Fast Fourier transform (FFT); Fourier transform Coulomb wave function 210, 240 Courant condition 838, 841, 843, 845 multidimensional 855 Courant-Friedrichs-Lewy stability criterion see Courant condition Covariance a priori 705 in general linear least squares 673, 677 matrix, by Cholesky decomposition 98, 673 matrix, of errors 805, 817 matrix, is inverse of Hessian matrix 685 matrix, when it is meaningful 695ff. in nonlinear models 685, 687 relation to chi-square 695ff. from singular value decomposition (SVD) 698 in straight line fitting 663 CR method see Cyclic reduction (CR) Cramer’s V 631 Crank-Nicolson method 848, 853, 855 CRC (cyclic redundancy check) 896ff. CRC-12 898 CRC-16 polynomial 898 CRC-CCITT 898 Creativity, essay on 8 Critical (Nyquist) sampling 500, 550 Cross (denotes matrix outer product) 73 Crosstabulation analysis 629 see also Contingency table Crout’s algorithm 44ff., 53 Cubic equations 183ff., 367 Cubic spline interpolation 113ff. see also Spline Cumulative binomial distribution 226, 229 Cumulative Poisson function 221 related to incomplete gamma function 221 Curvature matrix see Hessian matrix cvector() utility 943 Cycle, in multigrid method 874 Cyclic Jacobi method 466 Cyclic reduction (CR) 857f., 861f. Cyclic redundancy check (CRC) 896ff. Cyclic tridiagonal systems 74f. Danielson-Lanczos lemma 504f., 532 Data assigning keys to 897 continuous vs. binned 620 entropy 632ff., 903f. essay on 609 fitting 656ff. fraudulent 661 glitches in 659 iid (independent and identically distributed) 691 modeling 656ff. serial port 899 smoothing 610, 650ff. statistical tests 609ff