General Index Accelerated convergence of series 166ff. schedule 445 Accuracy 28f. thermodynamic analogy 444f. achievable in minimization 398,404,410 traveling salesman problem 445ff. achievable in root finding 353 ANSI C standard 2f.,14,25,930,941 contrasted with fidelity 841,849 ANSI macro 17,930 CPU different from memory 186 Antonov-Saleev variant of Sobol'sequence vs.stability 710,736,839,853 310E Acknowledgments xii Apple xvii Adams-Bashford-Moulton method 749 Macintosh 894 Adams'stopping criterion 373 Approximate inverse of matrix 57 Adaptive integration 129,141.709.714ff.. Approximation of functions 105f. 725ff,733f,737,744,749f,797 by Chebyshev polynomials 191f,519 Adaptive Monte Carlo integration 316ff., Pade approximant 200ff. 319f by rational functions 204ff Addition,multiple precision 916 by wavelets 601f..791 Addition theorem,elliptic integrals 262 see also Fitting ADI (altemating direction implicit)method Arguments,conversion of data types 24f.,930 856.870f.915 Arithmetic Adjoint operator 876 arbitrary precision 889.915ff. Adobe Illustrator xiii,xvii complex 23f.,948ff. Advective equation 835 floating point 889 AGM (arithmetic geometric mean)915 IEEE standard 285,890f Airy function 210,240.250 rounding 890 routine for 250f. Arithmetic coding 889,910ff. Aitken's delta squared process 166 Arithmetic-geometric mean (AGM)method Aitken's interpolation algorithm 108 915 Algorithms,non-numerical 889ff. Array Aliasing 501,576 centered subarray of 119 see also Fourier transform how to allocate 19 All-poles model 573 index range 18 see also Maximum entropy method(MEM) one-dimensional 18 All-zeros model 573 relation to C pointer 18 see also Periodogram three-dimensional 23 Allocation of storage 19,21f.,940ff. two-dimensional 20f. Alternating-direction implicit method (ADI) unit-offset 18,940f. 856.870f,915 variable dimension 20 Alternating series 166f zero-offset 18 Alternative extended Simpson's rule 134 Artificial viscosity 840,846 Amoeba 410 Ascending transformation,elliptic integrals see also Simplex,method of Nelder and 262 Mead ASCII character set 5,896,903,910 Amplification factor 837.839.841,849,854f Assembly language 278 Amplitude error 840 Associated Legendre polynomials 252f.,773 Analog-to-digital converter 821,894 recurrence relation for 253 Analyticity 201 relation to Legendre polynomials 252 Analyze/factorize/operate package 71f.,833 Association,measures of 610,628ff. Anderson-Darling statistic 626f. Asymptotic series 167 Andrew's sine 702 exponential integral 224 Annealing,method of simulated 394f.,444ff. Attenuation factors 590 assessment 454f. Autocorrelation for continuous variables 444,451f. in linear prediction 565 965General Index Accelerated convergence of series 166ff. Accuracy 28f. achievable in minimization 398, 404, 410 achievable in root finding 353 contrasted with fidelity 841, 849 CPU different from memory 186 vs. stability 710, 736, 839, 853 Acknowledgments xii Adams-Bashford-Moulton method 749 Adams’ stopping criterion 373 Adaptive integration 129, 141, 709, 714ff., 725ff., 733f., 737, 744, 749f., 797 Adaptive Monte Carlo integration 316ff., 319ff. Addition, multiple precision 916 Addition theorem, elliptic integrals 262 ADI (alternating direction implicit) method 856, 870f., 915 Adjoint operator 876 Adobe Illustrator xiii, xvii Advective equation 835 AGM (arithmetic geometric mean) 915 Airy function 210, 240, 250 routine for 250f. Aitken’s delta squared process 166 Aitken’s interpolation algorithm 108 Algorithms, non-numerical 889ff. Aliasing 501, 576 see also Fourier transform All-poles model 573 see also Maximum entropy method (MEM) All-zeros model 573 see also Periodogram Allocation of storage 19, 21f., 940ff. Alternating-direction implicit method (ADI) 856, 870f., 915 Alternating series 166f. Alternative extended Simpson’s rule 134 Amoeba 410 see also Simplex, method of Nelder and Mead Amplification factor 837, 839, 841, 849, 854f. Amplitude error 840 Analog-to-digital converter 821, 894 Analyticity 201 Analyze/factorize/operate package 71f., 833 Anderson-Darling statistic 626f. Andrew’s sine 702 Annealing, method of simulated 394f., 444ff. assessment 454f. for continuous variables 444, 451f. schedule 445 thermodynamic analogy 444f. traveling salesman problem 445ff. ANSI C standard 2f., 14, 25, 930, 941 ANSI macro 17, 930 Antonov-Saleev variant of Sobol’ sequence 310ff. Apple xvii Macintosh 894 Approximate inverse of matrix 57 Approximation of functions 105f. by Chebyshev polynomials 191f., 519 Pade approximant 200ff. ´ by rational functions 204ff. by wavelets 601f., 791 see also Fitting Arguments, conversion of data types 24f., 930 Arithmetic arbitrary precision 889, 915ff. complex 23f., 948ff. floating point 889 IEEE standard 285, 890f. rounding 890 Arithmetic coding 889, 910ff. Arithmetic-geometric mean (AGM) method 915 Array centered subarray of 119 how to allocate 19 index range 18 one-dimensional 18 relation to C pointer 18 three-dimensional 23 two-dimensional 20f. unit-offset 18, 940f. variable dimension 20 zero-offset 18 Artificial viscosity 840, 846 Ascending transformation, elliptic integrals 262 ASCII character set 5, 896, 903, 910 Assembly language 278 Associated Legendre polynomials 252f., 773 recurrence relation for 253 relation to Legendre polynomials 252 Association, measures of 610, 628ff. Asymptotic series 167 exponential integral 224 Attenuation factors 590 Autocorrelation in linear prediction 565 965