Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in FORTRAN77 :: Электронная библиотека попечительского совета мехмата МГУ

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Press W.H., Teukolsky S.A., Vetterling W.T. — Numerical recipes in FORTRAN77

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Название: Numerical recipes in FORTRAN77

Авторы: Press W.H., Teukolsky S.A., Vetterling W.T.

Язык:

Рубрика: Математика/Численные методы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1992

Количество страниц: 973

Добавлена в каталог: 01.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Linear algebraic equations LU decomposition      34ff. 195 386 732 783 786 801 1016 1022 1325f.
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)      51ff. 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 N-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. 431ff. 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 $\mathbf A^{-1}\cdot\mathbf B$       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 Pade 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
L’Ecuyer’s long period random generator errors on fitted parameters      1288 1290
L’Ecuyer’s long period random generator weighted      1285
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 Pade 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 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 equations      see “Linear algebraic equaequations”
Matrix finite differencing of partial differential equations      821ff.
Matrix finite differencing of partial differential equations inverse by Schultz’s method      49 598
Matrix get diagonal      985 1005 1226f. 1366 1381f.
Matrix Hermitian      450 454 475
Matrix Hermitian conjugate      450
Matrix Hessenberg      94 453 470 476ff. 488 1231ff.
Matrix hierarchically band diagonal      598
Matrix Hilbert      83
Matrix identity      25
Matrix ill- conditioned      53 56 114
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 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 Matrix square root of      423 455
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”; “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 51ff. 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 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 algorithms for image restoration      815f.
Maximum entropy method Bayesian      816f.
Maximum entropy method Cornwell — Evans algorithm      816
Maximum entropy method demystified      814
Maximum entropy method for inverse problems      809ff.
Maximum entropy method historic vs. Bayesian      816f.
Maximum entropy method image restoration      809ff.
Maximum entropy method intrinsic correlation function (ICF) model      817
Maximum entropy method 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 (MEM)”
Memory leak      953 956 1071 1327
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 for inverse problems      797
merge construct for straight line fitting      656 698
merge construct for straight line fitting, errors in both coordinates      660 1286
merge construct in general linear least squares      665
merge construct nonlinear models      675
merge construct parallelization      1011
Merge — with — dummy — values idiom      1090
Merit function      650
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.

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