Index 981 Jacobian 738 see also Linear prediction lower triangular 43f,96,790 Maximum likelihood estimate (M-estimates) multiplication denoted by dot 33 695,699f norm 58 and Bayes'Theorem 820 normal 457,458 chi-square test 695 nullity 61 defined 658 nullspace34,61,63,456,804 how to compute 702f orthogonal 98,457,470,594 mean absolute deviation 701,703 orthogonal transformation 459,470ff.,477 relation to least squares 658 orthonormal basis 66,100 Maxwell's equations 835 outer product denoted by 73,427 Mean(s) partitioning for determinant 78 of distribution 610f.,614 partitioning for inverse 77f. statistical differences between two 615ff. pattern multiply of sparse 81f. Mean absolute deviation of distribution 611, positive definite 35,96,674 701 QR decomposition 98f.,389,393,674 related to median 703 range 61 Measurement errors 656 rank 61 Median 329 residual 57 calculating 341 row and column indices 33 of distribution 611,614f. row vs.column operations 40f. as L-estimate 699 self-adjoint 457 role in robust straight line fitting 703 similarity transform 459ff,463,483,485 by selection 703 488 Median-of-three,in Quicksort 333 singular61,63,66,456 MEM see Maximum entropy method(MEM) singular value decomposition 34f,59ff., Memory,allocating and freeing 19,21f., 806 940正. sparse33,71ff,78,606,739,762,813 Merit function 656 special forms 35 in general linear least squares 671 splitting in relaxation method 865f. for inverse problems 806 spread 817 nonlinear models 681 square root of 430.462 for straight line fitting 662,703 storage schemes in C 20f.,33f,940ff. for straight line fitting,errors in both coor- submatrix of 22.945 dinates 666 symmetric35,96,457,461,469E,674 Mesh-drift instability 843f. 793f. Mesokurtic distribution 612 threshold multiply of sparse 81ff. Method of regularization 808ff. Toeplitz 90,92ff,201 Metropolis algorithm 445f transpose of sparse 80f. Microsoft xvii triangular 460 Midpoint method see Modified midpoint method; tridiagonal35,50f,71,115,156,460 Semi-implicit midpoint rule 461,469f,475f,494,848f,862, Mikado,or Town of Titipu 720 870f Miller's algorithm 181,234 tridiagonal with fringes 831 Minimal solution of recurrence relation 179 unitary 457 Minimax polynomial 192.204 updating 100,389f. Minimax rational function 204 upper triangular 43f..98 Minimization 394ff. Vandermonde 90ff.,120 along a ray84,384f,396,412f,418f see also Eigensystems 424.425 Matrix equations see Linear algebraic equa annealing,method of simulated 394f.. tions 444E matrix()utility 943f bracketing of minimum 397ff.,409 Matterhorn 612 Brent's method 396,402ff.,406,666 Maximization see Minimization Broyden-Fletcher-Goldfarb-Shanno algo- Maximum entropy method(MEM)572ff. rithm 397,426ff. algorithms for image restoration 824f. chi-square 659ff.,681ff. Bayesian 825f. choice of methods 395ff. Cornwell-Evans algorithm 825 combinatorial 444 demystified 823 conjugate gradient method 396f.,420ff. historic vs.Bayesian 825f 812f,824 image restoration 818ff. convergence rate 400,415f. intrinsic correlation function (ICF)model Davidon-Fletcher-Powell algorithm 397, 826 426f for inverse problems 818ff. degenerate 804 operation count 574 direction-set methods 396,412ffIndex 981 Jacobian 738 lower triangular 43f., 96, 790 multiplication denoted by dot 33 norm 58 normal 457, 458 nullity 61 nullspace 34, 61, 63, 456, 804 orthogonal 98, 457, 470, 594 orthogonal transformation 459, 470ff., 477 orthonormal basis 66, 100 outer product denoted by ⊗ 73, 427 partitioning for determinant 78 partitioning for inverse 77f. pattern multiply of sparse 81f. positive definite 35, 96, 674 QR decomposition 98f., 389, 393, 674 range 61 rank 61 residual 57 row and column indices 33 row vs. column operations 40f. self-adjoint 457 similarity transform 459ff., 463, 483, 485, 488 singular 61, 63, 66, 456 singular value decomposition 34f., 59ff., 806 sparse 33, 71ff., 78, 606, 739, 762, 813 special forms 35 splitting in relaxation method 865f. spread 817 square root of 430, 462 storage schemes in C 20f., 33f., 940ff. submatrix of 22, 945 symmetric 35, 96, 457, 461, 469ff., 674, 793f. threshold multiply of sparse 81ff. Toeplitz 90, 92ff., 201 transpose of sparse 80f. triangular 460 tridiagonal 35, 50f., 71, 115, 156, 460, 461, 469ff., 475ff., 494, 848f., 862, 870f. tridiagonal with fringes 831 unitary 457 updating 100, 389f. upper triangular 43f., 98 Vandermonde 90ff., 120 see also Eigensystems Matrix equations see Linear algebraic equa￾tions matrix() utility 943f. Matterhorn 612 Maximization see Minimization Maximum entropy method (MEM) 572ff. algorithms for image restoration 824f. Bayesian 825f. Cornwell-Evans algorithm 825 demystified 823 historic vs. Bayesian 825f. image restoration 818ff. intrinsic correlation function (ICF) model 826 for inverse problems 818ff. operation count 574 see also Linear prediction Maximum likelihood estimate (M-estimates) 695, 699ff. and Bayes’ Theorem 820 chi-square test 695 defined 658 how to compute 702f. mean absolute deviation 701, 703 relation to least squares 658 Maxwell’s equations 835 Mean(s) of distribution 610f., 614 statistical differences between two 615ff. Mean absolute deviation of distribution 611, 701 related to median 703 Measurement errors 656 Median 329 calculating 341 of distribution 611, 614f. as L-estimate 699 role in robust straight line fitting 703 by selection 703 Median-of-three, in Quicksort 333 MEM see Maximum entropy method (MEM) Memory, allocating and freeing 19, 21f., 940ff. Merit function 656 in general linear least squares 671 for inverse problems 806 nonlinear models 681 for straight line fitting 662, 703 for straight line fitting, errors in both coor￾dinates 666 Mesh-drift instability 843f. Mesokurtic distribution 612 Method of regularization 808ff. Metropolis algorithm 445f. Microsoft xvii Midpoint method see Modified midpoint method; Semi-implicit midpoint rule Mikado, or Town of Titipu 720 Miller’s algorithm 181, 234 Minimal solution of recurrence relation 179 Minimax polynomial 192, 204 Minimax rational function 204 Minimization 394ff. along a ray 84, 384f., 396, 412f., 418f., 424, 425 annealing, method of simulated 394f., 444ff. bracketing of minimum 397ff., 409 Brent’s method 396, 402ff., 406, 666 Broyden-Fletcher-Goldfarb-Shanno algo￾rithm 397, 426ff. chi-square 659ff., 681ff. choice of methods 395ff. combinatorial 444 conjugate gradient method 396f., 420ff., 812f., 824 convergence rate 400, 415f. Davidon-Fletcher-Powell algorithm 397, 426f. degenerate 804 direction-set methods 396, 412ff