메뉴 건너뛰기




Volumn 28, Issue 3, 2006, Pages 667-681

Generalized Hadamard product and the derivatives of spectral functions

Author keywords

Eigenvalues; Higher order derivatives; Multilinear algebra; Perturbation theory; Spectral function; Symmetric function; Twice differentiable

Indexed keywords

ALGEBRA; EIGENVALUES AND EIGENFUNCTIONS; PERTURBATION TECHNIQUES;

EID: 34247890899     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/050623206     Document Type: Article
Times cited : (9)

References (20)
  • 1
    • 22144463757 scopus 로고
    • ∞ Chevalley's theorem
    • ∞ Chevalley's theorem, Adv. in Math., 44 (1982), pp. 121-131.
    • (1982) Adv. in Math , vol.44 , pp. 121-131
    • DADOK, J.1
  • 2
    • 0011376467 scopus 로고
    • All convex invariant functions of hermitian matrices
    • C. DAVIS, All convex invariant functions of hermitian matrices, Arch. Math., 8 (1957), pp. 276-278.
    • (1957) Arch. Math , vol.8 , pp. 276-278
    • DAVIS, C.1
  • 3
    • 0003862232 scopus 로고
    • 2nd ed, Grundlehren Math. Wiss. 132, Springer-Verlag, New York, Berlin
    • T. KATO, Perturbation Theory for Linear Operators, 2nd ed., Grundlehren Math. Wiss. 132, Springer-Verlag, New York, Berlin, 1976.
    • (1976) Perturbation Theory for Linear Operators
    • KATO, T.1
  • 6
    • 0030304775 scopus 로고    scopus 로고
    • Convex analysis on the Hermitian matrices
    • A. S. LEWIS, Convex analysis on the Hermitian matrices, SIAM J. Optim., 6 (1996), pp. 164-177.
    • (1996) SIAM J. Optim , vol.6 , pp. 164-177
    • LEWIS, A.S.1
  • 7
    • 0030205038 scopus 로고    scopus 로고
    • Derivatives of spectral functions
    • A. S. LEWIS, Derivatives of spectral functions, Math. Oper. Res., 21 (1996), pp. 576-588.
    • (1996) Math. Oper. Res , vol.21 , pp. 576-588
    • LEWIS, A.S.1
  • 8
    • 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
  • 9
    • 3242887511 scopus 로고    scopus 로고
    • The mathematics of eigenvalue optimization
    • A. S. LEWIS, The mathematics of eigenvalue optimization, Math. Program., 97 (2003), pp. 155-176.
    • (2003) Math. Program , vol.97 , pp. 155-176
    • LEWIS, A.S.1
  • 10
    • 0042602157 scopus 로고    scopus 로고
    • Eigenvalue optimization
    • A. S. LEWIS AND M. L. OVERTON, Eigenvalue optimization, Acta Numer., 5 (1996), pp. 149-190.
    • (1996) Acta Numer , vol.5 , pp. 149-190
    • LEWIS, A.S.1    OVERTON, M.L.2
  • 11
    • 0036057564 scopus 로고    scopus 로고
    • Twice differentiable spectral functions
    • A. S. LEWIS AND H. S. SENDOV, Twice differentiable spectral functions, SIAM J. Matrix Anal. Appl., 23 (2001), pp. 368-386.
    • (2001) SIAM J. Matrix Anal. Appl , vol.23 , pp. 368-386
    • LEWIS, A.S.1    SENDOV, H.S.2
  • 12
    • 34247852577 scopus 로고    scopus 로고
    • Quadratic expansions of spectral functions
    • A. S. LEWIS AND H. S. SENDOV, Quadratic expansions of spectral functions, Linear Algebra Appl., 340 (2002), pp. 97-121.
    • (2002) Linear Algebra Appl , vol.340 , pp. 97-121
    • LEWIS, A.S.1    SENDOV, H.S.2
  • 13
    • 3142782148 scopus 로고    scopus 로고
    • Semismoothness of spectral functions
    • H. QI AND X. YANG, Semismoothness of spectral functions, SIAM J. Matrix Anal. Appl., 25 (2004), pp. 766-783.
    • (2004) SIAM J. Matrix Anal. Appl , vol.25 , pp. 766-783
    • QI, H.1    YANG, X.2
  • 14
    • 0031529488 scopus 로고    scopus 로고
    • Convex analysis of spectrally defined matrix functions
    • A. SEEGER, Convex analysis of spectrally defined matrix functions, SIAM J. Optim., 7 (1997), pp. 679-696.
    • (1997) SIAM J. Optim , vol.7 , pp. 679-696
    • SEEGER, A.1
  • 15
    • 33746138132 scopus 로고    scopus 로고
    • Interactions between the Generalized Hadamard Product and the Eigenvalues of Symmetric Matrices
    • Mathematical Series 2004-309, Department of Mathematics and Statistics, University of Guelph, Ontario
    • H. S. SENDOV, Interactions between the Generalized Hadamard Product and the Eigenvalues of Symmetric Matrices, Research report, Mathematical Series 2004-309, Department of Mathematics and Statistics, University of Guelph, Ontario, 2004.
    • (2004) Research report
    • SENDOV, H.S.1
  • 16
    • 34547213482 scopus 로고    scopus 로고
    • On the Higher-Order Derivatives of Spectral Functions: Two Special Cases
    • Mathematical Series 2004-310, Department of Mathematics and Statistics, University of Guelph, Ontario, Canada
    • H. S. SENDOV, On the Higher-Order Derivatives of Spectral Functions: Two Special Cases, Research report, Mathematical Series 2004-310, Department of Mathematics and Statistics, University of Guelph, Ontario, Canada, 2004.
    • (2004) Research report
    • SENDOV, H.S.1
  • 18
    • 34547182564 scopus 로고    scopus 로고
    • Second-Order Epi-differentiability and Subdifferentiability of Spectral Convex Functions, personal communication, 1999
    • M. TORKI, Second-Order Epi-differentiability and Subdifferentiability of Spectral Convex Functions, personal communication, 1999.
    • TORKI, M.1
  • 19
    • 21344492539 scopus 로고
    • On analyticity of functions involving eigenvalues
    • N.-K. TSING, M. K. H. FAN, AND E. I. VERRIEST, On analyticity of functions involving eigenvalues, Linear Algebra Appl., 207 (1994), pp. 159-180.
    • (1994) Linear Algebra Appl , vol.207 , pp. 159-180
    • TSING, N.-K.1    FAN, M.K.H.2    VERRIEST, E.I.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.