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| Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in Fortran 90 |
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| Предметный указатель |
Linear algebraic equations, nonsingular 23
Linear algebraic equations, overdetermined 25f. 199 670 797
Linear algebraic equations, partitioned 70
Linear algebraic equations, QR decomposition 91f. 382 386 668 1039f. 1199
Linear algebraic equations, row vs. column elimination 31f.
Linear algebraic equations, Schultz’s method 49 598
Linear algebraic equations, Sherman — Morrison formula 65ff. 83
Linear algebraic equations, singular 22 53 58 199 670
Linear algebraic equations, singular value decomposition (SVD) 51f. 199f. 670ff. 797 1022 1081 1290
Linear algebraic equations, sparse 23 43 63ff. 732 804 1020f. 1030
Linear algebraic equations, summary of tasks 25f.
Linear algebraic equations, Toeplitz 82 85ff. 195 1038
Linear algebraic equations, tridiagonal 26 42f. 64 109 150 453f. 462ff. 469ff. 488 839f. 853 861f. 1018f. 1227ff.
Linear algebraic equations, Vandermonde 82ff. 114 1037 1047
Linear algebraic equations, wavelet solution 597ff. 782
Linear algebraic equations, Woodbury formula 68ff. 83
Linear congruential random number generator 267ff. 1142
Linear congruential random number generator, choice of constants for 274ff.
Linear constraints 423
Linear convergence 346 393
Linear correlation (statistics) 630ff. 1276
Linear dependency, constructing orthonormal basis 58 94
Linear dependency, in linear algebraic equations 22f.
Linear dependency, of directions in  -dimensional space 409
Linear equations see Differential equations; Integral equations; Linear algebraic equations
Linear inversion method, constrained 799ff.
Linear prediction 557ff.
Linear prediction, characteristic polynomial 559
Linear prediction, coefficients 557ff. 1256
Linear prediction, compared to maximum entropy method 558
Linear prediction, compared with regularization 801
Linear prediction, contrasted to polynomial extrapolation 560
Linear prediction, related to optimal filtering 558
Linear prediction, removal of bias in 563
Linear prediction, stability 559f. 1257
Linear predictive coding (LPC) 563ff.
Linear programming 387 423ff. 1216ff.
Linear programming, artificial variables 429
Linear programming, auxiliary objective function 430
Linear programming, basic variables 426
Linear programming, composite simplex algorithm 435
Linear programming, constraints 423
Linear programming, convergence criteria 432
Linear programming, degenerate feasible vector 429
Linear programming, dual problem 435
Linear programming, equality constraints 423
Linear programming, feasible basis vector 426
Linear programming, feasible vector 424
Linear programming, fundamental theorem 426
Linear programming, inequality constraints 423
Linear programming, left-hand variables 426
Linear programming, nonbasic variables 426
Linear programming, normal form 426
Linear programming, objective function 424
Linear programming, optimal feasible vector 424
Linear programming, pivot element 428f.
Linear programming, primal problem 435
Linear programming, primal-dual algorithm 435
Linear programming, reduction to normal form 429ff.
Linear programming, restricted normal form 426ff.
Linear programming, revised simplex method 435
Linear programming, right-hand variables 426
Linear programming, simplex method 402 423ff. 431f. 1216ff.
Linear programming, slack variables 429
Linear programming, tableau 427
Linear programming, vertex of simplex 426
Linear recurrence see Recurrence relation
Linear regression 655ff. 660ff. 1285ff.
Linear regularization 799ff.
LINPACK 26
Literal constant 937 1361
little-endian 293
Local extrapolation 709
Local extremum 387f. 437
Localization of roots see Bracketing
Logarithmic function 255
Lomb periodogram method of spectral analysis 569f. 1258f.
Lomb periodogram method of spectral analysis, fast algorithm 574f. 1259
Loops 9f.
Lorentzian probability distribution 282 696f.
Low-pass filter 551 644f. 1283f.
Lower subscript 944
lower_triangle() utility function 989 1007 1200
LP coefficients see Linear prediction
LPC (linear predictive coding) 563ff.
LU decomposition 34ff. 47f. 51 55 64 97 374 667 732 1016 1022
LU decomposition, backsubstitution 39 1017
LU decomposition, band diagonal matrix 43ff. 1020
LU decomposition, complex equations 41f.
LU decomposition, Crout’s algorithm 36ff. 45 1017
LU decomposition, for  40
LU decomposition, for integral equations 783 786 1325f.
LU decomposition, for inverse iteration of eigenvectors 488
LU decomposition, for inverse problems 801
LU decomposition, for matrix determinant 41
LU decomposition, for matrix inverse 40 1016
LU decomposition, for nonlinear sets of equations 374 386 1196
LU decomposition, for Pad approximant 195 1080
LU decomposition, for Toeplitz matrix 87
LU decomposition, operation count 36 39
LU decomposition, outer product Gaussian elimination 1017
LU decomposition, pivoting 37f. 1017
LU decomposition, repeated backsubstitution 40 46
LU decomposition, solution of linear algebraic equations 40 1017
LU decomposition, solution of normal equations 667
Lucifer 290
L’Ecuyer’s long period random generator 271 273
M&R (Metcalf and Reid) 935
M-estimates 694ff.
M-estimates, how to compute 697f.
M-estimates, local 695ff. (see also Maximum likelihood estimate)
Machine accuracy 19f. 881f. 1189 1343
Macintosh, see Apple Macintosh
Maehly’s procedure 364 371
Magic in MEM image restoration 814
Magic in Pad approximation 195
Mantissa in floating point format 19 882 909 1343
Marginals 624
Marquardt method (least squares fitting) 678ff. 816 1292f.
Marsaglia shift register 1142 1148ff.
Marsaglia, G. 1142 1149
Mask 1006f. 1102 1200 1226 1305 1333f. 1368 1378 1382
mask, optional argument 948
mask, optional argument, facilitates parallelism 967f. 1038
Mass, center of 295ff.
MasterCard checksum 894
Mathematical Center (Amsterdam) 353
Mathematical intrinsic functions 946 951f.
matmul() intrinsic function 945 949 969 1026 1040 1050 1076 1200 1216 1290 1326
Matrix 23ff.
Matrix equations see Linear algebraic equations
Matrix, add vector to diagonal 1004 1234 1366 1381
Matrix, and integral equations 779 783 1325
Matrix, approximation of 58f. 598f.
Matrix, band diagonal 42ff. 64 1019
Matrix, band triangular 64
Matrix, banded 26 454
Matrix, bidiagonal 52
Matrix, block diagonal 64 754
Matrix, block triangular 64
Matrix, block tridiagonal 64
Matrix, bordered 64
Matrix, characteristic polynomial 449 469
Matrix, Cholesky decomposition 89f. 423 455 668 1038f.
Matrix, column augmented 28 1014
Matrix, complex 41
Matrix, condition number 53 78
Matrix, create unit matrix 1006 1382
Matrix, curvature 677
Matrix, cyclic banded 64
| Matrix, cyclic tridiagonal 67 1030
Matrix, defective 450 476 489
Matrix, design (fitting) 645 665 801 1082
Matrix, determinant of 25 41
Matrix, diagonal of sparse matrix 1033ff.
Matrix, diagonalization 452ff. 1225ff.
Matrix, elementary row and column operations 28f.
Matrix, finite differencing of partial differential equations 821f.
Matrix, get diagonal 985 1005 1226f. 1366 1381f.
Matrix, hermitian 450 454 475
Matrix, Hermitian conjugate 450
Matrix, Hessenberg 94 453 470 476ff. 488 1231f.
Matrix, Hessian see Hessian matrix
Matrix, hierarchically band diagonal 598
Matrix, Hilbert 83
Matrix, identity 25
Matrix, ill-conditioned 53
Matrix, indexed storage of 71f. 1030
Matrix, inverse 25 27 34 40 65ff. 70 95ff. 1014 1016f.
Matrix, inverse by Hotelling’s method 49 598
Matrix, inverse by Schultz’s method 49 598
Matrix, inverse multiplied by a matrix 40
Matrix, inverse, approximate 49
Matrix, iteration for inverse 49 598
Matrix, Jacobi transformation 453 456ff. 462 1225f.
Matrix, Jacobian 731 1309
Matrix, logical dimension 24
Matrix, lower triangular 34f. 89 781 1016
Matrix, lower triangular mask 1007 1200 1382
Matrix, multiplication denoted by dot 23
Matrix, multiplication, intrinsic function 949 969 1026 1040 1050 1200 1326
Matrix, norm 50
Matrix, normal 450ff.
Matrix, nullity 53
Matrix, nullspace 25 53f. 449 795
Matrix, of derivatives see Hessian matrix; Jacobian determinant
Matrix, orthogonal 91 450 463ff. 587
Matrix, orthogonal transformation 452 463ff. 469 1227
Matrix, orthonormal basis 58 94
Matrix, outer product denoted by cross 66 420
Matrix, partitioning for determinant 70
Matrix, partitioning for inverse 70
Matrix, pattern multiply of sparse 74
Matrix, physical dimension 24
Matrix, positive definite 26 89f. 668 1038
Matrix, QR decomposition 91f. 382 386 668 1039 1199
Matrix, range 53
Matrix, rank 53
Matrix, residual 49
Matrix, row and column indices 23
Matrix, row vs. column operations 31f.
Matrix, self-adjoint 450
Matrix, set diagonal elements 1005 1200 1366 1382
Matrix, similarity transform 452ff. 456 476 478 482
Matrix, singular 53f. 58 449
Matrix, singular value decomposition 26 51f. 797
Matrix, sparse 23 63ff. 71 598 732 754 804 1030ff.
Matrix, special forms 26
Matrix, splitting in relaxation method 856f.
Matrix, spread 808
Matrix, square root of 423 455
Matrix, symmetric 26 89 450 454 462ff. 668 785 1038 1225 1227
Matrix, threshold multiply of sparse 74 1031
Matrix, Toeplitz 82 85ff. 195 1038
Matrix, transpose of sparse 73f. 1033
Matrix, transpose() intrinsic function 950
Matrix, triangular 453
Matrix, tridiagonal 26 42f. 64 109 150 453f. 462ff. 469ff. 488 839f. 853 861f. 1018f. 1227ff.
Matrix, tridiagonal with fringes 822
Matrix, unitary 450
Matrix, updating 94 382 386 1041 1199
Matrix, upper triangular 34f. 91 1016
Matrix, upper triangular mask 1006 1226 1305 1382
Matrix, Vandermonde 82ff. 114 1037 1047
Matterhorn 606
maxexponent() intrinsic function 1107
Maximization see Minimization
Maximum entropy method (MEM) 565ff. 1258
Maximum entropy method (MEM), algorithms for image restoration 815f.
Maximum entropy method (MEM), Bayesian 816f.
Maximum entropy method (MEM), Cornwell — Evans algorithm 816
Maximum entropy method (MEM), demystified 814
Maximum entropy method (MEM), for inverse problems 809ff.
Maximum entropy method (MEM), historic vs. Bayesian 816f.
Maximum entropy method (MEM), image restoration 809ff.
Maximum entropy method (MEM), intrinsic correlation function (ICF) model 817
Maximum entropy method (MEM), operation count 567 (see also Linear prediction)
Maximum likelihood estimate (M-estimates) 690 694ff.
Maximum likelihood estimate (M-estimates), and Bayes’ Theorem 811
Maximum likelihood estimate (M-estimates), chi-square test 690
Maximum likelihood estimate (M-estimates), defined 652
Maximum likelihood estimate (M-estimates), how to compute 697f.
Maximum likelihood estimate (M-estimates), mean absolute deviation 696 698 1294
Maximum likelihood estimate (M-estimates), relation to least squares 652
maxloc() intrinsic function 949 992f. 1015
maxloc() intrinsic function, modified in Fortran 95 961
maxval() intrinsic function 945 948 961 1016 1273
Maxwell’s equations 825f.
Mean absolute deviation of distribution 605 696 1294
Mean absolute deviation of distribution, related to median 698
Mean(s) of distribution 604f. 608f. 1269
Mean(s), statistical differences between two 609ff. 1269f.
Measurement errors 650
Median 320
Median, as L-estimate 694
Median, by selection 698 1294
median, calculating 333
Median, of distribution 605 608f.
Median, role in robust straight line fitting 698
Median-of-three, in Quicksort 324
MEM see Maximum entropy method
Memory Management 938 941f. 953ff. 1327 1336
merge construct 945 950 1099f.
merge construct, contrasted with where 1023
merge construct, for conditional scalar expression 1010 1094f.
merge construct, parallelization 1011
Merge-with-dummy-values idiom 1090
Merit function 650
Merit function, for inverse problems 797
Merit function, for straight line fitting 656 698
Merit function, for straight line fitting, errors in both coordinates 660 1286
Merit function, in general linear least squares 665
Merit function, nonlinear models 675
Mesh-drift instability 834f.
Mesokurtic distribution 606
Metcalf, Michael 2/viii (see also M&R)
Method of regularization 799ff.
Metropolis algorithm 437f. 1219
Microsoft 1/xxii 2/xix
Microsoft Fortran Powerstation 2/viii
Midpoint method see Modified midpoint method; Semi-implicit midpoint rule
Mikado, or Town of Titipu 714
Miller’s algorithm 175 228 1106
MIMD machines (Multiple Instruction Multiple Data) 964 985 1071 1084
Minimal solution of recurrence relation 174
Minimax polynomial 186 198 1076
Minimax rational function 198
Minimization 387ff.
Minimization, along a ray 77 376f. 389 406ff. 412f. 415f. 418 1195f. 1211 1213
Minimization, and root finding 375
Minimization, annealing, method of simulated 387f. 436ff. 1219ff.
Minimization, bracketing of minimum 390ff. 402 1201f.
Minimization, Brent’s method 389 395ff. 399 660f. 1204ff. 1286
Minimization, Broyden — Fletcher — Goldfarb — Shanno algorithm 390 418ff. 1215
Minimization, by searching smaller subspaces 815
Minimization, chi-square 653ff. 675ff. 1285 1292
Minimization, choice of methods 388f.
Minimization, combinatorial 436f. 1219
Minimization, conjugate gradient method 390 413ff. 804 815 1210 1214
Minimization, convergence rate 393 409
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