972 Index special matrices 461 nonnormal 659.695,699ff. termination criterion 489f.495 relative truncation 883 tridiagonal matrix 460,475ff.,494 roundoff 185,889f. Eigenvalue and eigenvector,defined 456 series,advantage of an even 138f.,723 Eigenvalue problem for differential equations systematic vs.statistical 659 756.772f,779,781 truncation30,186,406,715,889f Eigenvalues and polynomial root finding 375 varieties found by check digits 902 EISPACK 461,482 varieties of,in PDEs 840ff. Electromagnetic potential 525 see also Roundoff error Elimination see Gaussian elimination Error function 220f.,607 Ellipse in confidence limit estimation 693 approximation via sampling theorem 6071 Elliptic integrals 261ff.,915 Chebyshev approximation 220f. addition theorem 262 complex 259 Carlson's forms and algorithms 261ff. for Fisher's z-transformation 638 Cauchy principal value 263 relation to Dawson's integral 259 duplication theorem 262f. relation to Fresnel integrals 255 Legendre 261ff.,267ff. relation to incomplete gamma function routines for 264ff. 220 symmetric form 261f routine for 220f. Weierstrass 262 for significance of correlation 636 Elliptic partial differential equations 827 for sum squared difference of ranks 641 alternating-direction implicit method (ADI) Error handling in programs 2,940 870f.915 Estimation of parameters see Fitting;Maxi- analyze/factorize/operate package 833 mum likelihood estimate biconjugate gradient method 833 Estimation of power spectrum 549ff.,572ff. boundary conditions 828f. Euler equation (fluid flow)840 comparison of rapid methods 863 Euler-Maclaurin summation formula 138,142 conjugate gradient method 833 Euler's constant 223f..257 cyclic reduction 857f.,861f. Euler's method for differential equations 708, Fourier analysis and cyclic reduction (FACR) 710.735 857E,863 Euler's transformation 166ff. Gauss-Seidel method 864.873.874f..884 generalized form 168f. incomplete Cholesky conjugate gradient Evaluation of functions see Function method (ICCG)833 Even and odd parts,of continued fraction Jacobi's method 864f.,873 172,217,222 matrix methods 833 Even parity 896 multigrid method 833.871ff. Exception handling in programs 2,940 rapid (Fourier)method 833,857ff exit()function 2 relaxation method 832.863ff. Explicit differencing 836 strongly implicit procedure 833 Exponent in floating point format 28.890 successive over-relaxation (SOR)866ff., Exponential deviate 287f. 871,875 Exponential integral 222f Emacs.GNU xiii asymptotic expansion 224 Embedded Runge-Kutta method 715f.,738 continued fraction 222 Encapsulation,in programs 6f. recurrence relation 178 Encryption 300 related to incomplete gamma function 222 Entropy 903f. relation to cosine integral 257 of data 632ff.,820 routine for En()223f. EOM(end of message)910 routine for Ei(r）225 Equality constraints 431 series 222 Equations Exponential probability distribution 577 cubic 183ff.,367 Extended midpoint rule 130f,135,141f. normal (fitting)651,672ff.,809f. Extended Simpson's rule 134,796,799 quadratic 29,183ff. Extended Simpson's three-eighths rule 797 see also Differential equations;Partial dif- Extended trapezoidal rule 131f.,133,136ff., ferential equations;Root finding 141,795 Equivalence classes 345f. roundoff error 138 Equivalence transformation 172 extern storage class 25 Error Extirpolation (so-called)581f. checksums for preventing 899 Extrapolation 105ff. clocking 899 in Bulirsch-Stoer method 724ff.,731 double exponential distribution 701 differential equations 708 local truncation 883 by linear prediction 564ff. Lorentzian distribution 701f. local 715 in multigrid method 872 maximum entropy method as type of 574972 Index special matrices 461 termination criterion 489f., 495 tridiagonal matrix 460, 475ff., 494 Eigenvalue and eigenvector, defined 456 Eigenvalue problem for differential equations 756, 772ff., 779, 781 Eigenvalues and polynomial root finding 375 EISPACK 461, 482 Electromagnetic potential 525 Elimination see Gaussian elimination Ellipse in confidence limit estimation 693 Elliptic integrals 261ff., 915 addition theorem 262 Carlson’s forms and algorithms 261ff. Cauchy principal value 263 duplication theorem 262f. Legendre 261ff., 267ff. routines for 264ff. symmetric form 261f. Weierstrass 262 Elliptic partial differential equations 827 alternating-direction implicit method (ADI) 870f., 915 analyze/factorize/operate package 833 biconjugate gradient method 833 boundary conditions 828f. comparison of rapid methods 863 conjugate gradient method 833 cyclic reduction 857f., 861f. Fourier analysis and cyclic reduction (FACR) 857ff., 863 Gauss-Seidel method 864, 873, 874f., 884 incomplete Cholesky conjugate gradient method (ICCG) 833 Jacobi’s method 864f., 873 matrix methods 833 multigrid method 833, 871ff. rapid (Fourier) method 833, 857ff. relaxation method 832, 863ff. strongly implicit procedure 833 successive over-relaxation (SOR) 866ff., 871, 875 Emacs, GNU xiii Embedded Runge-Kutta method 715f., 738 Encapsulation, in programs 6f. Encryption 300 Entropy 903f. of data 632ff., 820 EOM (end of message) 910 Equality constraints 431 Equations cubic 183ff., 367 normal (fitting) 651, 672ff., 809f. quadratic 29, 183ff. see also Differential equations; Partial dif￾ferential equations; Root finding Equivalence classes 345f. Equivalence transformation 172 Error checksums for preventing 899 clocking 899 double exponential distribution 701 local truncation 883 Lorentzian distribution 701f. in multigrid method 872 nonnormal 659, 695, 699ff. relative truncation 883 roundoff 185, 889f. series, advantage of an even 138f., 723 systematic vs. statistical 659 truncation 30, 186, 406, 715, 889f. varieties found by check digits 902 varieties of, in PDEs 840ff. see also Roundoff error Error function 220f., 607 approximation via sampling theorem 607f. Chebyshev approximation 220f. complex 259 for Fisher’s z-transformation 638 relation to Dawson’s integral 259 relation to Fresnel integrals 255 relation to incomplete gamma function 220 routine for 220f. for significance of correlation 636 for sum squared difference of ranks 641 Error handling in programs 2, 940 Estimation of parameters see Fitting; Maxi￾mum likelihood estimate Estimation of power spectrum 549ff., 572ff. Euler equation (fluid flow) 840 Euler-Maclaurin summation formula 138, 142 Euler’s constant 223f., 257 Euler’s method for differential equations 708, 710, 735 Euler’s transformation 166ff. generalized form 168f. Evaluation of functions see Function Even and odd parts, of continued fraction 172, 217, 222 Even parity 896 Exception handling in programs 2, 940 exit() function 2 Explicit differencing 836 Exponent in floating point format 28, 890 Exponential deviate 287f. Exponential integral 222ff. asymptotic expansion 224 continued fraction 222 recurrence relation 178 related to incomplete gamma function 222 relation to cosine integral 257 routine for En(x) 223f. routine for Ei(x) 225 series 222 Exponential probability distribution 577 Extended midpoint rule 130f., 135, 141f. Extended Simpson’s rule 134, 796, 799 Extended Simpson’s three-eighths rule 797 Extended trapezoidal rule 131f., 133, 136ff., 141, 795 roundoff error 138 extern storage class 25 Extirpolation (so-called) 581f. Extrapolation 105ff. in Bulirsch-Stoer method 724ff., 731 differential equations 708 by linear prediction 564ff. local 715 maximum entropy method as type of 574