메뉴 건너뛰기




Volumn 4, Issue 2, 2009, Pages 349-364

Conditions for strong ellipticity and M-eigenvalues

Author keywords

Elasticity tensor; M eigenvalue; Strong ellipticity; Z eigenvalue

Indexed keywords


EID: 63949087720     PISSN: 16733452     EISSN: 16733576     Source Type: Journal    
DOI: 10.1007/s11464-009-0016-6     Document Type: Article
Times cited : (92)

References (28)
  • 1
    • 0032612381 scopus 로고    scopus 로고
    • High-order contrasts for independent component analysis
    • J. F. Cardoso 1999 High-order contrasts for independent component analysis Neural Computation 11 157 192
    • (1999) Neural Computation , vol.11 , pp. 157-192
    • Cardoso, J.F.1
  • 2
    • 49349104328 scopus 로고    scopus 로고
    • Perron-Frobenius theorem for nonnegative tensors
    • K. C. Chang K. Pearson T. Zhang 2008 Perron-Frobenius theorem for nonnegative tensors Commu Math Sci 6 507 520
    • (2008) Commu Math Sci , vol.6 , pp. 507-520
    • Chang, K.C.1    Pearson, K.2    Zhang, T.3
  • 4
    • 33750978683 scopus 로고    scopus 로고
    • Spectral decomposition of a 4th-order covariance tensor: Applications to diffusion tensor MRI
    • P. J. Basser S. Pajevic 2007 Spectral decomposition of a 4th-order covariance tensor: Applications to diffusion tensor MRI Signal Processing 87 220 236
    • (2007) Signal Processing , vol.87 , pp. 220-236
    • Basser, P.J.1    Pajevic, S.2
  • 7
    • 0016576297 scopus 로고
    • On the ellipticity of the equations of non-linear elastostatics for a special material
    • J. K. Knowles E. Sternberg 1975 On the ellipticity of the equations of non-linear elastostatics for a special material J Elasticity 5 341 361
    • (1975) J Elasticity , vol.5 , pp. 341-361
    • Knowles, J.K.1    Sternberg, E.2
  • 8
    • 0017428499 scopus 로고
    • On the failure of ellipticity of the equations for finite elastostatic plane strain
    • J. K. Knowles E. Sternberg 1977 On the failure of ellipticity of the equations for finite elastostatic plane strain Arch Ration Mech Anal 63 321 336
    • (1977) Arch Ration Mech Anal , vol.63 , pp. 321-336
    • Knowles, J.K.1    Sternberg, E.2
  • 9
    • 0036018642 scopus 로고    scopus 로고
    • On the best rank-1 approximation of higher-order supersymmetric tensors
    • E. Kofidis P. A. Regalia 2002 On the best rank-1 approximation of higher-order supersymmetric tensors SIAM J Matrix Anal Appl 23 863 884
    • (2002) SIAM J Matrix Anal Appl , vol.23 , pp. 863-884
    • Kofidis, E.1    Regalia, P.A.2
  • 10
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problems of moments
    • J. B. Lasserre 2001 Global optimization with polynomials and the problems of moments SIAM Journal on Optimization 11 796 817
    • (2001) SIAM Journal on Optimization , vol.11 , pp. 796-817
    • Lasserre, J.B.1
  • 14
    • 33846621614 scopus 로고    scopus 로고
    • The degree of the E-characteristic polynomial of an even order tensor
    • G. Ni L. Qi F. Wang Y. Wang 2007 The degree of the E-characteristic polynomial of an even order tensor J Math Anal Appl 329 1218 1229
    • (2007) J Math Anal Appl , vol.329 , pp. 1218-1229
    • Ni, G.1    Qi, L.2    Wang, F.3    Wang, Y.4
  • 15
    • 1542266056 scopus 로고    scopus 로고
    • Semidefinite programming relaxation for semialgebraic Problems
    • P. A. Parrilo 2003 Semidefinite programming relaxation for semialgebraic Problems Mathematical Programming 96 293 320
    • (2003) Mathematical Programming , vol.96 , pp. 293-320
    • Parrilo, P.A.1
  • 16
    • 27744582534 scopus 로고    scopus 로고
    • Eigenvalues of a real supersymmetric tensor
    • L. Qi 2005 Eigenvalues of a real supersymmetric tensor J Symbolic Computation 40 1302 1324
    • (2005) J Symbolic Computation , vol.40 , pp. 1302-1324
    • Qi, L.1
  • 17
    • 33750796673 scopus 로고    scopus 로고
    • Rank and eigenvalues of a supersymmetric tensor, a multivariate homogeneous polynomial and an algebraic surface defined by them
    • L. Qi 2006 Rank and eigenvalues of a supersymmetric tensor, a multivariate homogeneous polynomial and an algebraic surface defined by them J Symbolic Computation 41 1309 1327
    • (2006) J Symbolic Computation , vol.41 , pp. 1309-1327
    • Qi, L.1
  • 18
    • 33750335770 scopus 로고    scopus 로고
    • Eigenvalues and invariants of tensors
    • L. Qi 2007 Eigenvalues and invariants of tensors J Math Anal Appl 325 1363 1377
    • (2007) J Math Anal Appl , vol.325 , pp. 1363-1377
    • Qi, L.1
  • 19
    • 35348819515 scopus 로고    scopus 로고
    • Numerical multilinear algebra and its applications
    • L. Qi W. Sun Y. Wang 2007 Numerical multilinear algebra and its applications Frontiers of Mathematics in China 2 4 501 526
    • (2007) Frontiers of Mathematics in China , vol.2 , Issue.4 , pp. 501-526
    • Qi, L.1    Sun, W.2    Wang, Y.3
  • 20
    • 58149504770 scopus 로고    scopus 로고
    • Z-eigenvalue methods for a global polynomial optimization problem
    • L. Qi F. Wang Y. Wang 2009 Z-eigenvalue methods for a global polynomial optimization problem Mathematical Programming 118 301 316
    • (2009) Mathematical Programming , vol.118 , pp. 301-316
    • Qi, L.1    Wang, F.2    Wang, Y.3
  • 22
    • 0025531963 scopus 로고
    • Ellipticity and deformations with discontinuous deformation gradients in finite elastostatics
    • P. Rosakis 1990 Ellipticity and deformations with discontinuous deformation gradients in finite elastostatics Arch Ration Mech Anal 109 1 37
    • (1990) Arch Ration Mech Anal , vol.109 , pp. 1-37
    • Rosakis, P.1
  • 23
    • 0020905805 scopus 로고
    • On copositive matrices and strong ellipticity for isotropic elastic materials
    • H. C. Simpson S. J. Spector 1983 On copositive matrices and strong ellipticity for isotropic elastic materials Arch Rational Mech Anal 84 55 68
    • (1983) Arch Rational Mech Anal , vol.84 , pp. 55-68
    • Simpson, H.C.1    Spector, S.J.2
  • 24
    • 0001635791 scopus 로고
    • Elements of a mathematical theory of elasticity
    • W. Thomson 1856 Elements of a mathematical theory of elasticity Philos Trans R Soc 166 481
    • (1856) Philos Trans R Soc , vol.166 , pp. 481
    • Thomson, W.1
  • 25
    • 63949085572 scopus 로고
    • 9th Ed. Adam and Charles Black London, Edingburgh
    • Thomson W (Lord Kelvin). Elasticity. Encyclopedia Briannica, Vol 7. 9th Ed. London, Edingburgh: Adam and Charles Black, 1878, 796-825
    • (1878) Elasticity. Encyclopedia Briannica , pp. 796-825
    • Thomson, W.1
  • 26
    • 0030181609 scopus 로고    scopus 로고
    • A reformulation of the strong ellipticity conditions for unconstrained hyperelastic media
    • Y. Wang M. Aron 1996 A reformulation of the strong ellipticity conditions for unconstrained hyperelastic media Journal of Elasticity 44 89 96
    • (1996) Journal of Elasticity , vol.44 , pp. 89-96
    • Wang, Y.1    Aron, M.2
  • 28
    • 0036056838 scopus 로고    scopus 로고
    • Rank-1 approximation of higher-order tensors
    • T. Zhang G. H. Golub 2001 Rank-1 approximation of higher-order tensors SIAM J Matrix Anal Appl 23 534 550
    • (2001) SIAM J Matrix Anal Appl , vol.23 , pp. 534-550
    • Zhang, T.1    Golub, G.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.