980 Index convergence criteria 439 how to compute 702f. degenerate feasible vector 436 local 700ff. dual problem 443 see also Maximum likelihood estimate equality constraints 431 Machine accuracy 28f.,890 feasible basis vector 433f Macintosh,see Apple Macintosh feasible vector 431 Maehly's procedure 370,378 fundamental theorem 432f Magic inequality constraints 431 in MEM image restoration 823 left-hand variables 434 in Pade approximation 201 nonbasic variables 434 Mantissa in floating point format 28.890, normal form 433 918 objective function 431 Marginals 630 optimal feasible vector 431 Marquardt method (least squares fitting)683ff., pivot element 435f. 825 primal-dual algorithm 443 Mass,center of 305ff. primal problem 443 MasterCard checksum 901f. reduction to normal form 436ff. Mathematical Center (Amsterdam)360 restricted normal form 433ff. Matrix 33ff. revised simplex method 443 allocating and freeing 21f,940ff. right-hand variables 434 approximation of 66f.,605f. simplex method 408f.,430,433ff.,439ff band diagonal 50,51ff.,71 slack variables 436 band triangular 71 tableau 434 banded 35,461 vertex of simplex 433 bidiagonal 60 Linear regression 661f,666f年 block diagonal 71,762 see also Fitting block triangular 71 Linear regularization 808ff. block tridiagonal 71 LINPACK 35 bordered 71 Little-endian 302 characteristic polynomial 456,475f. Local extrapolation 715 Cholesky decomposition 96ff,430,462. Local extremum 394.445 674 Localization of roots see Bracketing column augmented 37 Logarithmic function 262 compatibility 940 Lomb periodogram method of spectral analysis complex 49f. 576f condition number 61,85 fast algorithm 581f curvature 682 Loops 8 cyclic banded 71 Lorentzian probability distribution 292,701f. cyclic tridiagonal 74f. Low-pass filter 558,650 defective 457,482,494 LP coefficients see Linear prediction of derivatives see Hessian matrix;Jacobian LPC(linear predictive coding)571f. determinant LU decomposition 43ff.,56f.,59,63,71, design (fitting)651,671.809 104.381.673.739 determinant of 34,49 for A-1.B 48 diagonalization 459ff. band diagonal matrix 51ff.,53f. elementary row and column operations 37 complex equations 49f. finite differencing of partial differential Crout's algorithm 44ff.,53 equations 830ff. for integral equations 792,795 freeing a submatrix 23 for inverse iteration of eigenvectors 494 Hermitian 457,461,481f. for inverse problems 810 Hermitian conjugate 457 for matrix determinant 49 Hessenberg100,460,477,482,484f.,494 for matrix inverse 48 Hessian see Hessian matrix for nonlinear sets of equations 381.393 hierarchically band diagonal 606 operation count 44,48 Hilbert 90 for Pade approximant 201 identity 34 pivoting 45f. ill-conditioned 61.63,120 repeated backsubstitution 48.54 indexed storage of 78f. solution of linear algebraic equations 48 and integral equations 788,792 solution of normal equations 673 inverse34,36,42,48f.,73f,77E,102f for Toeplitz matrix 94 inverse,approximate 57 Lucifer (encryption algorithm)300 inverse by Hotelling's method 57.606 lvector()utility 943 inverse by Schultz's method 57,606 inverse multiplied by a matrix 49 iteration for inverse 57,606 M-estimates699f Jacobi transformation 460,463ff.,469980 Index convergence criteria 439 degenerate feasible vector 436 dual problem 443 equality constraints 431 feasible basis vector 433f. feasible vector 431 fundamental theorem 432f. inequality constraints 431 left-hand variables 434 nonbasic variables 434 normal form 433 objective function 431 optimal feasible vector 431 pivot element 435f. primal-dual algorithm 443 primal problem 443 reduction to normal form 436ff. restricted normal form 433ff. revised simplex method 443 right-hand variables 434 simplex method 408f., 430, 433ff., 439ff. slack variables 436 tableau 434 vertex of simplex 433 Linear regression 661ff., 666ff. see also Fitting Linear regularization 808ff. LINPACK 35 Little-endian 302 Local extrapolation 715 Local extremum 394, 445 Localization of roots see Bracketing Logarithmic function 262 Lomb periodogram method of spectral analysis 576f. fast algorithm 581f. Loops 8 Lorentzian probability distribution 292, 701f. Low-pass filter 558, 650 LP coefficients see Linear prediction LPC (linear predictive coding) 571f. LU decomposition 43ff., 56f., 59, 63, 71, 104, 381, 673, 739 for A−1 · B 48 band diagonal matrix 51ff., 53f. complex equations 49f. Crout’s algorithm 44ff., 53 for integral equations 792, 795 for inverse iteration of eigenvectors 494 for inverse problems 810 for matrix determinant 49 for matrix inverse 48 for nonlinear sets of equations 381, 393 operation count 44, 48 for Pade approximant 201 ´ pivoting 45f. repeated backsubstitution 48, 54 solution of linear algebraic equations 48 solution of normal equations 673 for Toeplitz matrix 94 Lucifer (encryption algorithm) 300 lvector() utility 943 M-estimates 699ff. how to compute 702f. local 700ff. see also Maximum likelihood estimate Machine accuracy 28f., 890 Macintosh, see Apple Macintosh Maehly’s procedure 370, 378 Magic in MEM image restoration 823 in Pade approximation 201 ´ Mantissa in floating point format 28, 890, 918 Marginals 630 Marquardt method (least squares fitting) 683ff., 825 Mass, center of 305ff. MasterCard checksum 901f. Mathematical Center (Amsterdam) 360 Matrix 33ff. allocating and freeing 21f., 940ff. approximation of 66f., 605f. band diagonal 50, 51ff., 71 band triangular 71 banded 35, 461 bidiagonal 60 block diagonal 71, 762 block triangular 71 block tridiagonal 71 bordered 71 characteristic polynomial 456, 475f. Cholesky decomposition 96ff., 430, 462, 674 column augmented 37 compatibility 940 complex 49f. condition number 61, 85 curvature 682 cyclic banded 71 cyclic tridiagonal 74f. defective 457, 482, 494 of derivatives see Hessian matrix; Jacobian determinant design (fitting) 651, 671, 809 determinant of 34, 49 diagonalization 459ff. elementary row and column operations 37 finite differencing of partial differential equations 830ff. freeing a submatrix 23 Hermitian 457, 461, 481f. Hermitian conjugate 457 Hessenberg 100, 460, 477, 482, 484f., 494 Hessian see Hessian matrix hierarchically band diagonal 606 Hilbert 90 identity 34 ill-conditioned 61, 63, 120 indexed storage of 78f. and integral equations 788, 792 inverse 34, 36, 42, 48f., 73ff., 77f., 102ff. inverse, approximate 57 inverse by Hotelling’s method 57, 606 inverse by Schultz’s method 57, 606 inverse multiplied by a matrix 49 iteration for inverse 57, 606 Jacobi transformation 460, 463ff., 469