메뉴 건너뛰기




Volumn 21, Issue 1, 2011, Pages 127-148

Minimizing the condition number of a Gram matrix

Author keywords

Condition number; Generalized gradient; Gram matrix; Interpolation; Least squares; Semismooth; Smoothing method; Spherical harmonics

Indexed keywords

CONDITION NUMBERS; GENERALIZED GRADIENT; GRAM MATRIX; LEAST SQUARE; SEMISMOOTH; SMOOTHING METHOD; SPHERICAL HARMONICS;

EID: 79957506054     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/100786022     Document Type: Article
Times cited : (46)

References (29)
  • 1
    • 79251473716 scopus 로고    scopus 로고
    • Well conditioned spherical designs for integration and interpolation on the two-sphere
    • C. AN, X. CHEN, I. H. SLOAN, AND R. S. WOMERSLEY, Well conditioned spherical designs for integration and interpolation on the two-sphere, SIAM J. Numer. Anal., 48 (2010), pp. 2135-2157.
    • (2010) SIAM J. Numer. Anal. , vol.48 , pp. 2135-2157
    • An, C.1    Chen, X.2    Sloan, I.H.3    Womersley, R.S.4
  • 2
    • 0034415996 scopus 로고    scopus 로고
    • The condition number of real Vandermonde, Krylov and positive definite Hankel matrices
    • B. BECKERMANN, The condition number of real Vandermonde, Krylov and positive definite Hankel matrices, Numer. Math., 85 (2000), pp. 553-577.
    • (2000) Numer. Math. , vol.85 , pp. 553-577
    • Beckermann, B.1
  • 5
    • 0035612967 scopus 로고    scopus 로고
    • Tensor product Gauss-Lobatto points are Fekete points for the cube
    • DOI 10.1090/S0025-5718-00-01262-X
    • L. BOS, M. A. TAYLOR, AND B. A. WINGATE, Tensor product Gauss-Lobatto points are Fekete points for the cube, Math. Comp., 70 (2000), pp. 1543-1547. (Pubitemid 33582382)
    • (2001) Mathematics of Computation , vol.70 , Issue.236 , pp. 1543-1547
    • Bos, L.1    Taylor, M.A.2    Wingate, B.A.3
  • 6
    • 0023416451 scopus 로고
    • Projected gradient method for linearly constrained problems
    • P. H. CALAMAI AND J. J. MORÉ, Projected gradient method for linearly constrained problems, Math. Program., 39 (1987), pp. 93-116.
    • (1987) Math. Program. , vol.39 , pp. 93-116
    • Calamai, P.H.1    Moré, J.J.2
  • 7
    • 85099494167 scopus 로고    scopus 로고
    • Computational existence proofs for spherical t-designs
    • to appear
    • X. CHEN, A. FROMMER, AND B. LANG, Computational existence proofs for spherical t-designs, Numer. Math., to appear.
    • Numer. Math.
    • Chen, X.1    Frommer, A.2    Lang, B.3
  • 8
    • 37849025487 scopus 로고    scopus 로고
    • Existence of solutions to systems of undetermined equations and spherical designs
    • X. CHEN AND R. S. WOMERSLEY, Existence of solutions to systems of undetermined equations and spherical designs, SIAM J. Numer. Anal., 44 (2006), pp. 2326-2341.
    • (2006) SIAM J. Numer. Anal. , vol.44 , pp. 2326-2341
    • Chen, X.1    Womersley, R.S.2
  • 9
    • 78149291090 scopus 로고    scopus 로고
    • Smoothing nonlinear conjugate gradient method for image restoration using nonsmooth nonconvex minimization
    • X. CHEN AND W. ZHOU, Smoothing nonlinear conjugate gradient method for image restoration using nonsmooth nonconvex minimization, SIAM J. Imaging Sci., 3 (2010), pp. 765-790.
    • (2010) SIAM J. Imaging Sci. , vol.3 , pp. 765-790
    • Chen, X.1    Zhou, W.2
  • 11
    • 34249922645 scopus 로고
    • Algorithms for generalized fractional programming
    • J. P. CROUZEIX AND J. A. FERLAND, Algorithms for generalized fractional programming, Math. Program., 52 (1991), pp. 191-207.
    • (1991) Math. Program. , vol.52 , pp. 191-207
    • Crouzeix, J.P.1    Ferland, J.A.2
  • 12
    • 0000181889 scopus 로고
    • On non-linear fractional programming
    • W. DINKELBACH, On non-linear fractional programming, Manag. Sci., 13 (1967), pp. 492-498.
    • (1967) Manag. Sci. , vol.13 , pp. 492-498
    • Dinkelbach, W.1
  • 13
    • 0000554369 scopus 로고    scopus 로고
    • Solution of monotone complementarity problems with locally Lipschitzian functions
    • PII S0025561096000597
    • A. FISCHER, Solution of monotone complementarity problems with locally Lipschitz functions, Math. Program., 76 (1997), pp. 513-532. (Pubitemid 127380006)
    • (1997) Mathematical Programming, Series B , vol.76 , Issue.3 , pp. 513-532
    • Fischer, A.1
  • 14
    • 0004236492 scopus 로고
    • 2nd ed., Johns Hopkins University Press, Baltimore, MD
    • G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 2nd ed., Johns Hopkins University Press, Baltimore, MD, 1993.
    • (1993) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 15
    • 0000223746 scopus 로고
    • Calculation of Gauss quadrature rules
    • G. H. GOLUB AND J. H. WELSCH, Calculation of Gauss quadrature rules, Math. Comp., 23 (1969), pp. 221-230.
    • (1969) Math. Comp. , vol.23 , pp. 221-230
    • Golub, G.H.1    Welsch, J.H.2
  • 17
    • 0003111058 scopus 로고    scopus 로고
    • Nonsmooth analysis of eigenvalues
    • A. S. LEWIS, Nonsmooth analysis of eigenvalues, Math. Program., 84 (1999), pp. 1-24.
    • (1999) Math. Program. , vol.84 , pp. 1-24
    • Lewis, A.S.1
  • 18
    • 70450205215 scopus 로고    scopus 로고
    • Optimizing condition numbers
    • P. MARÉCHAL AND J. J. YE, Optimizing condition numbers, SIAM J. Optim., 20 (2009), pp. 935-947.
    • (2009) SIAM J. Optim. , vol.20 , pp. 935-947
    • Maréchal, P.1    Ye, J.J.2
  • 19
    • 0000012763 scopus 로고
    • Semismooth and semiconvex functions in constrained optimization
    • R. MIFFLIN, Semismooth and semiconvex functions in constrained optimization, SIAM J. Control Optim., 15 (1977), pp. 959-972.
    • (1977) SIAM J. Control Optim. , vol.15 , pp. 959-972
    • Mifflin, R.1
  • 20
    • 17444406259 scopus 로고    scopus 로고
    • Smooth minimization of non-smooth functions
    • DOI 10.1007/s10107-004-0552-5
    • Y. NESTEROV, Smooth minimization of non-smooth functions, Math. Program., 103 (2005), pp. 127-152. (Pubitemid 40537674)
    • (2005) Mathematical Programming , vol.103 , Issue.1 , pp. 127-152
    • Nesterov, Yu.1
  • 21
    • 33947732413 scopus 로고    scopus 로고
    • Smoothing technique and its applications in semidefinite optimization
    • DOI 10.1007/s10107-006-0001-8
    • Y. NESTEROV, Smoothing technique and its applications in semidefinite optimization, Math. Program., 110 (2007), pp. 245-259. (Pubitemid 46504991)
    • (2007) Mathematical Programming , vol.110 , Issue.2 , pp. 245-259
    • Nesterov, Y.1
  • 22
    • 0003181133 scopus 로고
    • Large-scale optimization of eigenvalues
    • M. L. OVERTON, Large-scale optimization of eigenvalues, SIAM J. Optim., 2 (1992), pp. 88-120.
    • (1992) SIAM J. Optim. , vol.2 , pp. 88-120
    • Overton, M.L.1
  • 23
    • 0039907084 scopus 로고
    • On the sum of the largest eigenvalues of a symmetric matrix
    • M. L. OVERTON AND R. S. WOMERSLEY, On the sum of the largest eigenvalues of a symmetric matrix, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 41-45.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 41-45
    • Overton, M.L.1    Womersley, R.S.2
  • 24
    • 34250080273 scopus 로고
    • Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices
    • M. L. OVERTON AND R. S. WOMERSLEY, Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices, Math. Program., 62 (1993), pp. 321-357.
    • (1993) Math. Program. , vol.62 , pp. 321-357
    • Overton, M.L.1    Womersley, R.S.2
  • 25
    • 0031139858 scopus 로고    scopus 로고
    • First and second order analysis of nonlinear semidefinite programs
    • PII 80025561096000810
    • A. SHAPIRO, First and second order analysis of nonlinear semidefinite programs, Math. Program., 77 (1997), pp. 301-320. (Pubitemid 127412634)
    • (1997) Mathematical Programming, Series B , vol.77 , Issue.2 , pp. 301-320
    • Shapiro, A.1
  • 26
    • 69949158512 scopus 로고    scopus 로고
    • A variational characterisation of spherical designs
    • I. H. SLOAN AND R. S. WOMERSLEY, A variational characterisation of spherical designs, J. Approx. Theory, 159 (2009), pp. 308-318.
    • (2009) J. Approx. Theory , vol.159 , pp. 308-318
    • Sloan, I.H.1    Womersley, R.S.2
  • 27
    • 0346707472 scopus 로고    scopus 로고
    • Strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problems
    • D. SUN AND J. SUN, Strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problems, SIAM J. Numer. Anal., 40 (2002), pp. 2352-2367.
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 2352-2367
    • Sun, D.1    Sun, J.2
  • 28
    • 77956177876 scopus 로고    scopus 로고
    • Error bounds for approximation in Chebyshev points
    • S. XIANG, X. CHEN, AND H. WANG, Error bounds for approximation in Chebyshev points, Numer. Math., 116 (2010), pp. 463-491.
    • (2010) Numer. Math. , vol.116 , pp. 463-491
    • Xiang, S.1    Chen, X.2    Wang, H.3
  • 29
    • 70450260767 scopus 로고    scopus 로고
    • Smoothing projected gradient method and its application to stochastic linear complementarity problems
    • C. ZHANG AND X. CHEN, Smoothing projected gradient method and its application to stochastic linear complementarity problems, SIAM J. Optim., 20 (2009), pp. 627-649.
    • (2009) SIAM J. Optim. , vol.20 , pp. 627-649
    • Zhang, C.1    Chen, X.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.