968 Index for straight line fitting,errors in both coor- Complex systems of linear equations 49f. dinates 666 complex.c utility functions 23f..948ff. for two binned data sets 622 Compression of data 603,889,903ff.,910ff unequal size samples 623 Concordant pair for Kendall's tau 642f. Chip rate 300 Condition number 61,85 Chirp signal 563 Confidence level 692f.,696ff. Cholesky decomposition 96ff.,430.462 Confidence limits backsubstitution 97 bootstrap method 692f operation count 97 and chi-square 693f. pivoting 97 confidence region,confidence interval 692 solution of normal equations 674 on estimated model parameters 689ff. Circulant 592 by Monte Carlo simulation 689ff. Class,data type 7 from singular value decomposition (SVD) Clenshaw-Curtis quadrature 130,196,518 698 519 Confluent hypergeometric function 210,246 Clenshaw's recurrence formula 181ff.,196 Conjugate directions 414f.,421ff. for Chebyshev polynomials 193 Conjugate gradient method stability 181ff. biconjugate 84 Clocking errors 899 compared to variable metric method 425f. cn function 269 elliptic partial differential equations 833 Coarse-to-fine operator 873 for minimization 396f.,420ff.,812f,824 Coarse-grid correction 873f. minimum residual method 85 Coding preconditioner 85f. arithmetic 910ff. for sparse system 83ff.,606 checksums 896 and wavelets 606 decoding a Huffman-encoded message Conservative differential equations 732f 905 Constrained linear inversion method 808ff. Huffman 903ff. Constrained linear optimization see Linear pro- run-length 909 gramming variable length code 903 Constrained optimization 394 Ziv-Lempel 903 Constraints,deterministic 813ff. see also Arithmetic coding;Huffman cod- Constraints,linear 431 ing Contingency coefficient C 631 Coefficients Contingency table 628ff.,644 binomial 215 statistics based on chi-square 630f. for Gaussian quadrature 147ff. statistics based on entropy 632ff. for Gaussian quadrature,nonclassical weight continue construction 14 function 157ff.,797 Continued fraction 169ff. for quadrature formulas 131f,797 Bessel functions 240f. Column degeneracy 32 convergence criterion 171 Column operations on matrix 37,40f. equivalence transformation 172 Column totals 630 evaluation 169ff. Combinatorial minimization see Annealing evaluation along with normalization condi- Comite Consultatif Intemational Telegraphique tion 247 et Telephonique (CCITT)897f.,909 even and odd parts 172,217,222 Communication theory,use in adaptive integra- even part 255,257 tion 727 exponential integral 222 Communications protocol 896 Fresnel integral 255 Comparison function for rejection method incomplete beta function 227 290f incomplete gamma function 217 Complementary error function Lentz's method 171,219 see Error function modified Lentz's method 171 Complete elliptic integral see Elliptic integrals Pincherle's theorem 181 Complex arithmetic 23f.,176ff.,948ff. ratio of Bessel functions 246 avoidance of in path integration 209 rational function approximation 170,217, cubic equations 185 227 for linear equations 49f. recurrence for evaluating 170f. quadratic equations 184 and recurrence relation 181 Complex error function 259 sine and cosine integrals 257 Complex plane Steed's method 170f. fractal structure for Newton's rule 367f. tangent function 169 path integration for function evaluation typography for 169 208ff,271 Continuous variable (statistics)628 poles in11l,166,208f,213,561,573, Control structures 6,8ff. 724f bad 14968 Index for straight line fitting, errors in both coor￾dinates 666 for two binned data sets 622 unequal size samples 623 Chip rate 300 Chirp signal 563 Cholesky decomposition 96ff., 430, 462 backsubstitution 97 operation count 97 pivoting 97 solution of normal equations 674 Circulant 592 Class, data type 7 Clenshaw-Curtis quadrature 130, 196, 518, 519 Clenshaw’s recurrence formula 181ff., 196 for Chebyshev polynomials 193 stability 181ff. Clocking errors 899 cn function 269 Coarse-to-fine operator 873 Coarse-grid correction 873f. Coding arithmetic 910ff. checksums 896 decoding a Huffman-encoded message 905 Huffman 903ff. run-length 909 variable length code 903 Ziv-Lempel 903 see also Arithmetic coding; Huffman cod￾ing Coefficients binomial 215 for Gaussian quadrature 147ff. for Gaussian quadrature, nonclassical weight function 157ff., 797 for quadrature formulas 131ff., 797 Column degeneracy 32 Column operations on matrix 37, 40f. Column totals 630 Combinatorial minimization see Annealing Comite Consultatif International T ´ el´ egraphique ´ et Tel´ ephonique (CCITT) 897f., 909 ´ Communication theory, use in adaptive integra￾tion 727 Communications protocol 896 Comparison function for rejection method 290f. Complementary error function see Error function Complete elliptic integral see Elliptic integrals Complex arithmetic 23f., 176ff., 948ff. avoidance of in path integration 209 cubic equations 185 for linear equations 49f. quadratic equations 184 Complex error function 259 Complex plane fractal structure for Newton’s rule 367f. path integration for function evaluation 208ff., 271 poles in 111, 166, 208f., 213, 561, 573, 724f. Complex systems of linear equations 49f. complex.c utility functions 23f., 948ff. Compression of data 603, 889, 903ff., 910ff. Concordant pair for Kendall’s tau 642f. Condition number 61, 85 Confidence level 692f., 696ff. Confidence limits bootstrap method 692f. and chi-square 693f. confidence region, confidence interval 692 on estimated model parameters 689ff. by Monte Carlo simulation 689ff. from singular value decomposition (SVD) 698 Confluent hypergeometric function 210, 246 Conjugate directions 414f., 421ff. Conjugate gradient method biconjugate 84 compared to variable metric method 425f. elliptic partial differential equations 833 for minimization 396f., 420ff., 812f., 824 minimum residual method 85 preconditioner 85f. for sparse system 83ff., 606 and wavelets 606 Conservative differential equations 732f. Constrained linear inversion method 808ff. Constrained linear optimization see Linear pro￾gramming Constrained optimization 394 Constraints, deterministic 813ff. Constraints, linear 431 Contingency coefficient C 631 Contingency table 628ff., 644 statistics based on chi-square 630ff. statistics based on entropy 632ff. continue construction 14 Continued fraction 169ff. Bessel functions 240f. convergence criterion 171 equivalence transformation 172 evaluation 169ff. evaluation along with normalization condi￾tion 247 even and odd parts 172, 217, 222 even part 255, 257 exponential integral 222 Fresnel integral 255 incomplete beta function 227 incomplete gamma function 217 Lentz’s method 171, 219 modified Lentz’s method 171 Pincherle’s theorem 181 ratio of Bessel functions 246 rational function approximation 170, 217, 227 recurrence for evaluating 170f. and recurrence relation 181 sine and cosine integrals 257 Steed’s method 170f. tangent function 169 typography for 169 Continuous variable (statistics) 628 Control structures 6, 8ff. bad 14