메뉴 건너뛰기




Volumn 30, Issue 1, 2010, Pages 94-107

A preconditioned Newton algorithm for the nearest correlation matrix

Author keywords

Alternating projections method; Armijo line search conditions; Correlation matrix; Newton's method; Positive semidefinite matrix; Preconditioning; Rounding error

Indexed keywords

CONJUGATE GRADIENT METHOD; NEWTON-RAPHSON METHOD;

EID: 76549100532     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drn085     Document Type: Article
Times cited : (62)

References (22)
  • 2
    • 33646249113 scopus 로고    scopus 로고
    • Least-squares covariance matrix adjustments
    • BOYD, S. & XIAO, L. (2005) Least-squares covariance matrix adjustments. SIAM J. Matrix Anal. Appl., 27, 532-546.
    • (2005) SIAM J. Matrix Anal. Appl. , vol.27 , pp. 532-546
    • Boyd, S.1    Xiao, L.2
  • 3
    • 55549110811 scopus 로고    scopus 로고
    • Performance and accuracy of LAPACK's symmetric tridiagonal eigensolvers
    • DEMMEL, J. W., MARQUES, O. A., PARLETT, B. N. & VOMEL, C. (2008) Performance and accuracy of LAPACK's symmetric tridiagonal eigensolvers. SIAM J. Sci. Comput., 30, 1508-1526.
    • (2008) SIAM J. Sci. Comput. , vol.30 , pp. 1508-1526
    • Demmel, J.W.1    Marques, O.A.2    Parlett, B.N.3    Vomel, C.4
  • 6
    • 77950520532 scopus 로고    scopus 로고
    • A methodology to stress correlations
    • Fourth Quarter
    • FINGER, C. C. (1997) A methodology to stress correlations. RiskMetrics Monit., Fourth Quarter, 3-11.
    • (1997) Risk Metrics Monit , pp. 3-11
    • Finger, C.C.1
  • 8
    • 0000379660 scopus 로고
    • Computing a nearest symmetric positive semidefinite matrix
    • HIGHAM, N. J. (1988) Computing a nearest symmetric positive semidefinite matrix. Linear Algebra Appl., 103, 103-118.
    • (1988) Linear Algebra Appl , vol.103 , pp. 103-118
    • Higham, N.J.1
  • 9
    • 0036457301 scopus 로고    scopus 로고
    • 2nd edn. Philadelphia, PA: Society for Industrial and Applied Mathematics
    • HIGHAM, N. J. (2002a) Accuracy and Stability of Numerical Algorithms, 2nd edn. Philadelphia, PA: Society for Industrial and Applied Mathematics.
    • (2002) Accuracy and Stability of Numerical Algorithms
    • Higham, N.J.1
  • 10
    • 0344153904 scopus 로고    scopus 로고
    • Computing the nearest correlation matrix-A problem from finance
    • HIGHAM, N. J. (2002b) Computing the nearest correlation matrix-A problem from finance. IMA J. Numer. Anal., 22, 329-343.
    • (2002) IMA J. Numer. Anal. , vol.22 , pp. 329-343
    • Higham, N.J.1
  • 11
    • 0009371156 scopus 로고
    • Least-squares approximation of an improper correlation matrix by a proper one
    • KNOL, D. K. & TEN BERGE, J. M. F. (1989) Least-squares approximation of an improper correlation matrix by a proper one. Psychometrika, 54, 53-61.
    • (1989) Psychometrika , vol.54 , pp. 53-61
    • Knol, D.K.1    Ten Berge, J.M.F.2
  • 12
    • 0032002017 scopus 로고    scopus 로고
    • An approximate method for sampling correlated random variables from partially-specified distributions
    • LURIE, P. M. & GOLDBERG, M. S. (1998) An approximate method for sampling correlated random variables from partially-specified distributions. Manage. Sci., 44, 203-218.
    • (1998) Manage. Sci. , vol.44 , pp. 203-218
    • Lurie, P.M.1    Goldberg, M.S.2
  • 13
    • 14544268199 scopus 로고    scopus 로고
    • A dual approach to solve semidefinite least-squares problems
    • MALICK, J. (2004) A dual approach to solve semidefinite least-squares problems. SIAM J. Matrix Anal. Appl., 26, 272-284.
    • (2004) SIAM J. Matrix Anal. Appl. , vol.26 , pp. 272-284
    • Malick, J.1
  • 14
    • 0001036636 scopus 로고
    • Smoothing and interpolation in a convex subset of a Hilbert space
    • NAG Toolbox for MATLAB. Oxford: NAG Ltd. Available at
    • MICCHELLI, C. A. & UTRERAS, F. I. (1988) Smoothing and interpolation in a convex subset of a Hilbert space. SIAM J. Sci. Statist. Comput., 9, 728-746. NAG Toolbox for MATLAB. Oxford: NAG Ltd. Available at http://www.nag.co.uk/.
    • (1988) SIAM J. Sci. Statist. Comput. , vol.9 , pp. 728-746
    • Micchelli, C.A.1    Utreras, F.I.2
  • 15
    • 0016555955 scopus 로고
    • Solution of sparse indefinite systems of linear equations
    • PAIGE, C. C. & SAUNDERS, M. A. (1975) Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal., 12, 617-629.
    • (1975) SIAM J. Numer. Anal. , vol.12 , pp. 617-629
    • Paige, C.C.1    Saunders, M.A.2
  • 16
    • 34247364678 scopus 로고    scopus 로고
    • A quadratically convergent Newton method for computing the nearest correlation matrix
    • QI, H.-D. & SUN, D. (2006) A quadratically convergent Newton method for computing the nearest correlation matrix. SIAM J. Matrix Anal. Appl., 28, 360-385.
    • (2006) SIAM J. Matrix Anal. Appl. , vol.28 , pp. 360-385
    • Qi, H.-D.1    Sun, D.2
  • 19
    • 57249089431 scopus 로고    scopus 로고
    • An application of the nearest correlation matrix on web document classification
    • QI, H.-D., XIA, Z. & XING, G. (2007) An application of the nearest correlation matrix on web document classification. J. Indus. Manage. Optim., 3, 701-713.
    • (2007) J. Indus. Manage. Optim. , vol.3 , pp. 701-713
    • Qi, H.-D.1    Xia, Z.2    Xing, G.3
  • 20
    • 34547439695 scopus 로고    scopus 로고
    • An inexact primal-dual path following algorithm for convex quadratic SDP
    • TOH, K.-C. (2008) An inexact primal-dual path following algorithm for convex quadratic SDP. Math. Program., 112, 221-254.
    • (2008) Math. Program. , vol.112 , pp. 221-254
    • Toh, K.-C.1
  • 21
    • 58049214116 scopus 로고    scopus 로고
    • Correlation stress testing for value-at-risk
    • TURKAY, S., EPPERLEIN, E. & CHRISTOFIDES, N. (2003) Correlation stress testing for value-at-risk. J. Risk, 5, 75-89.
    • (2003) J. Risk , vol.5 , pp. 75-89
    • Turkay, S.1    Epperlein, E.2    Christofides, N.3
  • 22
    • 0002090018 scopus 로고
    • Condition numbers and equilibration of matrices
    • VAN DER SLUIS, A. (1969) Condition numbers and equilibration of matrices. Numer. Math., 14, 14-23.
    • (1969) Numer. Math. , vol.14 , pp. 14-23
    • Van Der Sluis, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.