982 Index downhill simplex method 396.408ff.. and Kolmogorov-Smirnov statistic 627, 451f,702f 646f finding best-fit parameters 656 partial differential equations 833 Fletcher-Reeves algorithm 396f.,421ff. quasi-random sequences in 309ff. functional 804 quick and dirty 691f. global 394f..451f..656 recursive 316ff.323ff globally convergent multidimensional 425f狂 significance of Lomb periodogram 578 golden section search 397ff.,403 simulation of data 660.689ff..695 multidimensional 395f.,408ff. stratified sampling 317f.,323 in nonlinear model fitting 681f. Moon,calculate phases of If.,13f. Polak-Ribiere algorithm 396f.,422f Mother functions 591 Powell's method 396,408,412ff. Mother Nature 689,691 quasi-Newton methods 383,397,425ff Moving average (MA)model 573 and root finding 382 Moving window averaging 650 scaling of variables 428 Mozart 8 by searching smaller subspaces 824 MS xvii steepest descent method 421,813 MS-DOS xii.3 termination criterion 398f,410 Muller's method 371,379 use in finding double roots 348 Multidimensional use for sparse linear systems 84ff. confidence levels of fitting 694 using derivatives 396f,405ff. data,use of binning 629 variable metric methods 397,425ff. Fourier transform 521ff. see also Linear programming Fourier transform,real data 525ff Minimum residual method,for sparse system initial value problems 853ff. 85 integrals 130,161ff.,304ff,316ff. MINPACK 688 interpolation 123ff. MIPS 894 Kolmogorov-Smimov test 645ff. Missing data problem 576 least squares fitting 680 Mississippi River 446,455 minimization 408ff..412ff.420f Mode of distribution 611,615 Monte Carlo integration 304ff.,316ff. Modeling of data see Fitting normal (Gaussian)distribution 695 Model-trust region 393,688 optimization 395f. partial differential equations 853ff. Modes,homogeneous,of recursive filters 561 root finding347f,365,377,379f,382 Modified Bessel functions see Bessel func- 754,757f,761,762 tions Modified Lentz's method,for continued frac- search using quasi-random sequence 309 secant method 380.389ff. tions 171 wavelet transform 602 Modified midpoint method 722f,726 Modified moments 158 Multigrid method 833,871ff. avoid SOR 875 Modula-2 7 boundary conditions 877f. Modular arithmetic,without overflow 278, 281,284 choice of operators 877 Modularization,in programs 6f. coarse-to-fine operator 873 coarse-grid correction 873f. Modulus of linear congruential generator 276 cycle 874 Moments dual viewpoint 883 of distribution 610ff. fine-to-coarse operator 873 filter that preserves 650 full approximation storage (FAS)algorithm modified problem of 158 882f problem of 90f. full multigrid method (FMG)872,877f. and quadrature formulas 799 full weighting 876 semi-invariants 614 Gauss-Seidel relaxation 874f. Monic polynomial 149 half weighting 876 Monotonicity constraint,in upwind differenc- importance of adjoint operator 876 ing 846 injection operator 873 Monte Carlo 162,275 interpolation operator 873 adaptive 316ff.,319ff. line relaxation 875 bootstrap method 691f. local truncation error 883 comparison of sampling methods 318f. Newton's rule 882,884 exploration of binary tree 300 nonlinear equations 882ff. importance sampling 316f. nonlinear Gauss-Seidel relaxation 884 integration 130,162,304ff.,316ff. odd-even ordering 875,878 integration,recursive 323ff. operation count 871 integration,using Sobol'sequence 313ff. prolongation operator 873 integration,VEGAS algorithm 319ff. recursive nature 874982 Index downhill simplex method 396, 408ff., 451f., 702f. finding best-fit parameters 656 Fletcher-Reeves algorithm 396f., 421ff. functional 804 global 394f., 451f., 656 globally convergent multidimensional 425ff. golden section search 397ff., 403 multidimensional 395f., 408ff. in nonlinear model fitting 681f. Polak-Ribiere algorithm 396f., 422f. Powell’s method 396, 408, 412ff. quasi-Newton methods 383, 397, 425ff. and root finding 382 scaling of variables 428 by searching smaller subspaces 824 steepest descent method 421, 813 termination criterion 398f., 410 use in finding double roots 348 use for sparse linear systems 84ff. using derivatives 396f., 405ff. variable metric methods 397, 425ff. see also Linear programming Minimum residual method, for sparse system 85 MINPACK 688 MIPS 894 Missing data problem 576 Mississippi River 446, 455 Mode of distribution 611, 615 Modeling of data see Fitting Model-trust region 393, 688 Modes, homogeneous, of recursive filters 561 Modified Bessel functions see Bessel func￾tions Modified Lentz’s method, for continued frac￾tions 171 Modified midpoint method 722f., 726 Modified moments 158 Modula-2 7 Modular arithmetic, without overflow 278, 281, 284 Modularization, in programs 6f. Modulus of linear congruential generator 276 Moments of distribution 610ff. filter that preserves 650 modified problem of 158 problem of 90f. and quadrature formulas 799 semi-invariants 614 Monic polynomial 149 Monotonicity constraint, in upwind differenc￾ing 846 Monte Carlo 162, 275 adaptive 316ff., 319ff. bootstrap method 691f. comparison of sampling methods 318f. exploration of binary tree 300 importance sampling 316f. integration 130, 162, 304ff., 316ff. integration, recursive 323ff. integration, using Sobol’ sequence 313ff. integration, VEGAS algorithm 319ff. and Kolmogorov-Smirnov statistic 627, 646f. partial differential equations 833 quasi-random sequences in 309ff. quick and dirty 691f. recursive 316ff., 323ff. significance of Lomb periodogram 578 simulation of data 660, 689ff., 695 stratified sampling 317f., 323 Moon, calculate phases of 1f., 13f. Mother functions 591 Mother Nature 689, 691 Moving average (MA) model 573 Moving window averaging 650 Mozart 8 MS xvii MS-DOS xii, 3 Muller’s method 371, 379 Multidimensional confidence levels of fitting 694 data, use of binning 629 Fourier transform 521ff. Fourier transform, real data 525ff. initial value problems 853ff. integrals 130, 161ff., 304ff., 316ff. interpolation 123ff. Kolmogorov-Smirnov test 645ff. least squares fitting 680 minimization 408ff., 412ff., 420ff. Monte Carlo integration 304ff., 316ff. normal (Gaussian) distribution 695 optimization 395f. partial differential equations 853ff. root finding 347ff., 365, 377, 379ff., 382, 754, 757f., 761, 762 search using quasi-random sequence 309 secant method 380, 389ff. wavelet transform 602 Multigrid method 833, 871ff. avoid SOR 875 boundary conditions 877f. choice of operators 877 coarse-to-fine operator 873 coarse-grid correction 873f. cycle 874 dual viewpoint 883 fine-to-coarse operator 873 full approximation storage (FAS) algorithm 882ff. full multigrid method (FMG) 872, 877f. full weighting 876 Gauss-Seidel relaxation 874f. half weighting 876 importance of adjoint operator 876 injection operator 873 interpolation operator 873 line relaxation 875 local truncation error 883 Newton’s rule 882, 884 nonlinear equations 882ff. nonlinear Gauss-Seidel relaxation 884 odd-even ordering 875, 878 operation count 871 prolongation operator 873 recursive nature 874