Index 967 equations;Two-point boundary value CCITT (Comite Consultatif International Tele- problems graphique et Telephonique)897f.909 Box-Muller algorithm for normal deviate 289 CCITT polynomial 897f. Bracketing Center of mass 305ff. of function minimum 350,397ff.,409 Central limit theorem 658f. of roots348.350f,360.369,371,376 Central tendency,measures of 610ff. 397 Change of variable Branch cut,for hypergeometric function 209f. in integration 144ff.,797 Branching 8 in Monte Carlo integration 307f. Break iteration 12f. in probability distribution 287ff. Brenner,N.M.506,522 Characteristic polynomial Brent's method digital filter 561 minimization 395f.,402ff.,666 minimization,using derivative 396,406 eigensystems 456,475f. linear prediction 567 root finding 348,356,666 matrix with a specified 375 Broyden-Fletcher-Goldfarb-Shanno algorithm of recurrence relation 180 397,426ft. Broyden's method 380,389ff.,393 Characteristics of partial differential equations 827 singular Jacobian 393 Chebyshev acceleration in successive over- Bubble sort 330 relaxation (SOR)868f. Bugs in compilers xiii Chebyshev approximation 91,130.189,190ff. Clenshaw-Curtis quadrature 196 how to report iv,xviii Clenshaw's recurrence formula 193 Bulirsch-Stoer coefficients for 191 algorithm for rational function interpolation 111f. contrasted with Pade approximation 201 method (differential equations)209.272. derivative of approximated function 189. 708f,712,722,724f,733,747 195 method (differential equations),stepsize economization of series 198ff.,201 control 725,733f. for error function 220f. for second order equations 733 even function 194 Burg's LP algorithm 568 and fast cosine transform 519 Byte 28 gamma functions 242 integral of approximated function 195 odd function 194 C+7,24 polynomial fits derived from 197 C(programming language)11 rational function 204ff. ANSI2f,14,25,930,941 Remes exchange algorithm for filter 560 C++7.24 Chebyshev polynomials 190ff. compilers 3 continuous orthonormality 190f. discrete orthonormality 191 control structures 5 deficiencies 16,24f.,26f. explicit formulas for 190 exteral functions 25 formula for x in terms of 199 Check digit 901 features 15f. function declaration 17 Checksum 889,896 function definition 17 cyclic redundancy (CRC)896ff. header (.h)file 17 Cherry,sundae without a 818 implicit conversions 24f,930 Chi-by-eye 657 Kernighan and Ritchie 2,16,24,930 Chi-square fitting see Fitting;Least squares nature of 15f. fitting Numerical Recipes in xv,I Chi-square probability function 216,221, operator associativity 25f. 621,660,806 operator precedence 25f. as boundary of confidence region 693f. prototypes 2,25,930 related to incomplete gamma function 221 vectors in 18 Chi-square test 620f. Calendar algorithms If.,11ff. for binned data 620f. Calibration 659 chi-by-eye 657 Cards,sorting a hand of 330 and confidence limit estimation 693f. Carlson's elliptic integrals 261f. for contingency table 630ff. Cash-Karp parameters 716f. degrees of freedom 621f. Cauchy probability distribution see Lorentzian for inverse problems 806 probability distribution least squares fitting 659ff. Cauchy problem for partial differential equa- nonlinear models 681ff. tions 827f. rule of thumb 661 Cayley's representation of exp(-iHt)853 for straight line fitting 661ff.Index 967 equations; Two-point boundary value problems Box-Muller algorithm for normal deviate 289 Bracketing of function minimum 350, 397ff., 409 of roots 348, 350ff., 360, 369, 371, 376, 397 Branch cut, for hypergeometric function 209f. Branching 8 Break iteration 12f. Brenner, N.M. 506, 522 Brent’s method minimization 395f., 402ff., 666 minimization, using derivative 396, 406 root finding 348, 356, 666 Broyden-Fletcher-Goldfarb-Shanno algorithm 397, 426ff. Broyden’s method 380, 389ff., 393 singular Jacobian 393 Bubble sort 330 Bugs in compilers xiii how to report iv, xviii Bulirsch-Stoer algorithm for rational function interpolation 111f. method (differential equations) 209, 272, 708f., 712, 722, 724ff., 733, 747 method (differential equations), stepsize control 725, 733f. for second order equations 733 Burg’s LP algorithm 568 Byte 28 C++ 7, 24 C (programming language) 11 ANSI 2f., 14, 25, 930, 941 C++ 7, 24 compilers 3 control structures 5 deficiencies 16, 24f., 26f. external functions 25 features 15f. function declaration 17 function definition 17 header (.h) file 17 implicit conversions 24f., 930 Kernighan and Ritchie 2, 16, 24, 930 nature of 15f. Numerical Recipes in xv, 1 operator associativity 25f. operator precedence 25f. prototypes 2, 25, 930 vectors in 18 Calendar algorithms 1f., 11ff. Calibration 659 Cards, sorting a hand of 330 Carlson’s elliptic integrals 261f. Cash-Karp parameters 716f. Cauchy probability distribution see Lorentzian probability distribution Cauchy problem for partial differential equa￾tions 827f. Cayley’s representation of exp(−iHt) 853 CCITT (Comite Consultatif International T ´ el´ e-´ graphique et Tel´ ephonique) 897f., 909 ´ CCITT polynomial 897f. Center of mass 305ff. Central limit theorem 658f. Central tendency, measures of 610ff. Change of variable in integration 144ff., 797 in Monte Carlo integration 307f. in probability distribution 287ff. Characteristic polynomial digital filter 561 eigensystems 456, 475f. linear prediction 567 matrix with a specified 375 of recurrence relation 180 Characteristics of partial differential equations 827 Chebyshev acceleration in successive over￾relaxation (SOR) 868f. Chebyshev approximation 91, 130, 189, 190ff. Clenshaw-Curtis quadrature 196 Clenshaw’s recurrence formula 193 coefficients for 191 contrasted with Pade approximation 201 ´ derivative of approximated function 189, 195 economization of series 198ff., 201 for error function 220f. even function 194 and fast cosine transform 519 gamma functions 242 integral of approximated function 195 odd function 194 polynomial fits derived from 197 rational function 204ff. Remes exchange algorithm for filter 560 Chebyshev polynomials 190ff. continuous orthonormality 190f. discrete orthonormality 191 explicit formulas for 190 formula for xk in terms of 199 Check digit 901 Checksum 889, 896 cyclic redundancy (CRC) 896ff. Cherry, sundae without a 818 Chi-by-eye 657 Chi-square fitting see Fitting; Least squares fitting Chi-square probability function 216, 221, 621, 660, 806 as boundary of confidence region 693f. related to incomplete gamma function 221 Chi-square test 620f. for binned data 620f. chi-by-eye 657 and confidence limit estimation 693f. for contingency table 630ff. degrees of freedom 621f. for inverse problems 806 least squares fitting 659ff. nonlinear models 681ff. rule of thumb 661 for straight line fitting 661ff