966 Index use of FFT 545 reflection formulas,modified functions Wiener-Khinchin theorem 498,574 247 AUTODIN-II polynomial 898 routines for 232ff.,243ff Autonomous differential equations 735f. routines for modified functions 248f. Autoregressive model (AR)see Maximum en- series for 166,230 tropy method(MEM) series for K 247 Average deviation of distribution 611 series for Y,242 Averaging kernel,in Backus-Gilbert method spherical 240,251 816 turning point 241 Wronskian 240.246 Best-fit parameters 656,662,666,703 Backsubstitution 42,47,50,98 see also Fitting in band diagonal matrix 54 Beta function 213 in Cholesky decomposition 97 incomplete see Incomplete beta function complex equations 49 BFGS algorithm see Broyden-Fletcher-Goldfarb- direct for computing A-1.B 48 Shanno algorithm relaxation solution of boundary value prob- Bias,of exponent 28 lems 764 Bias,removal in linear prediction 570 in singular value decomposition 64 Biconjugacy 84 Backtracking 427 Biconjugate gradient method in quasi-Newton methods 384 elliptic partial differential equations 833 Backus-Gilbert method 815ff preconditioning 85f.,833 Backward deflation 370 for sparse system 84f.,606 Bader-Deufthard method 737.742f. Bicubic interpolation 125f. Bairstow's method 371,376f. Bicubic spline 127f. Balancing 483 Band diagonal matrix 50,51ff Big-endian 302 Bilinear interpolation 123f backsubstitution 54 LU decomposition 53f. Binomial coefficients 213 multiply by vector 52f recurrences for 215 storage 52 Binomial probability function 215 Band-pass filter 558,562 cumulative 229 wavelets 592,599f. deviates from 290,295f. Bandwidth limited function 501 Binormal distribution 637,695 Bank accounts,checksum for 902 Biorthogonality 84 Bar codes,checksum for 902 Bisection 117,366 Bartlett window 554 compared to minimum bracketing 397f., 300f Base of representation 28,890 BASIC,Numerical Recipes in xv,1 minimum finding with derivatives 406 Basis functions in general linear least squares root finding350.353f.,359f.397.476 671 BISYNCH 898 Bayes'Theorem 819 Bit 28 Bayesian reversal in fast Fourier transform(FFT) approach to inverse problems 808,820, 505f,532 825f Bitwise logical functions 296ff.,898f. contrasted with frequentist 819 Block-by-block method 797 vs.historic maximum entropy method Block of statements 6 825f Bode's rule 132 views on straight line fitting 670 Boltzmann probability distribution 445 Bays'shuffle 280 Boltzmann's constant 445 Beroulli number 138 Bootstrap method 691f. Bessel functions 230ff.,240ff. Bordering method for Toeplitz matrix 92f. asymptotic form 230,236 Borwein and Borwein method for 915 complex 210 Boundary 161f..432f..753 continued fraction 240f,246f Boundary conditions double precision 230 for differential equations 707f. fractional order 230,240ff. initial value problems 708 Miller's algorithm 181,234 in multigrid method 877f. modified 236ff. partial differential equations 514,828ff., modified,fractional order 246ff. 857f modified,normalization formula 239,246 for spheroidal harmonics 774 modified,routines for 237ff two-point boundary value problems 708, normalization formula 181 753狂 recurrence relation 178,231,239,241f. Boundary value problems see Differential reflection formulas 242 equations;Elliptic partial differential966 Index use of FFT 545 Wiener-Khinchin theorem 498, 574 AUTODIN-II polynomial 898 Autonomous differential equations 735f. Autoregressive model (AR) see Maximum en￾tropy method (MEM) Average deviation of distribution 611 Averaging kernel, in Backus-Gilbert method 816 Backsubstitution 42, 47, 50, 98 in band diagonal matrix 54 in Cholesky decomposition 97 complex equations 49 direct for computing A−1 · B 48 relaxation solution of boundary value prob￾lems 764 in singular value decomposition 64 Backtracking 427 in quasi-Newton methods 384 Backus-Gilbert method 815ff. Backward deflation 370 Bader-Deuflhard method 737, 742f. Bairstow’s method 371, 376f. Balancing 483 Band diagonal matrix 50, 51ff. backsubstitution 54 LU decomposition 53f. multiply by vector 52f. storage 52 Band-pass filter 558, 562 wavelets 592, 599f. Bandwidth limited function 501 Bank accounts, checksum for 902 Bar codes, checksum for 902 Bartlett window 554 Base of representation 28, 890 BASIC, Numerical Recipes in xv, 1 Basis functions in general linear least squares 671 Bayes’ Theorem 819 Bayesian approach to inverse problems 808, 820, 825f. contrasted with frequentist 819 vs. historic maximum entropy method 825f. views on straight line fitting 670 Bays’ shuffle 280 Bernoulli number 138 Bessel functions 230ff., 240ff. asymptotic form 230, 236 complex 210 continued fraction 240f., 246f. double precision 230 fractional order 230, 240ff. Miller’s algorithm 181, 234 modified 236ff. modified, fractional order 246ff. modified, normalization formula 239, 246 modified, routines for 237ff. normalization formula 181 recurrence relation 178, 231, 239, 241f. reflection formulas 242 reflection formulas, modified functions 247 routines for 232ff., 243ff. routines for modified functions 248f. series for 166, 230 series for Kν 247 series for Yν 242 spherical 240, 251 turning point 241 Wronskian 240, 246 Best-fit parameters 656, 662, 666, 703 see also Fitting Beta function 213 incomplete see Incomplete beta function BFGS algorithm see Broyden-Fletcher-Goldfarb￾Shanno algorithm Bias, of exponent 28 Bias, removal in linear prediction 570 Biconjugacy 84 Biconjugate gradient method elliptic partial differential equations 833 preconditioning 85f., 833 for sparse system 84f., 606 Bicubic interpolation 125f. Bicubic spline 127f. Big-endian 302 Bilinear interpolation 123f. Binomial coefficients 213 recurrences for 215 Binomial probability function 215 cumulative 229 deviates from 290, 295f. Binormal distribution 637, 695 Biorthogonality 84 Bisection 117, 366 compared to minimum bracketing 397f., 399f. minimum finding with derivatives 406 root finding 350, 353f., 359ff., 397, 476 BISYNCH 898 Bit 28 reversal in fast Fourier transform (FFT) 505f., 532 Bitwise logical functions 296ff., 898f. Block-by-block method 797 Block of statements 6 Bode’s rule 132 Boltzmann probability distribution 445 Boltzmann’s constant 445 Bootstrap method 691f. Bordering method for Toeplitz matrix 92f. Borwein and Borwein method for π 915 Boundary 161f., 432f., 753 Boundary conditions for differential equations 707f. initial value problems 708 in multigrid method 877f. partial differential equations 514, 828ff., 857ff. for spheroidal harmonics 774 two-point boundary value problems 708, 753ff. Boundary value problems see Differential equations; Elliptic partial differential