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Volumn 329, Issue 2, 2007, Pages 1218-1229

The degree of the E-characteristic polynomial of an even order tensor

Author keywords

E Characteristic polynomial; E Eigenvalue; Resultant; Tensor; Upper bound

Indexed keywords


EID: 33846621614     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.07.064     Document Type: Article
Times cited : (72)

References (31)
  • 1
    • 0016472847 scopus 로고
    • Output feedback stabilization and related problems-solutions via decision methods
    • Anderson B.D., Bose N.K., and Jury E.I. Output feedback stabilization and related problems-solutions via decision methods. IEEE Trans. Automat. Control 20 (1975) 55-66
    • (1975) IEEE Trans. Automat. Control , vol.20 , pp. 55-66
    • Anderson, B.D.1    Bose, N.K.2    Jury, E.I.3
  • 3
    • 0017012938 scopus 로고
    • General procedure for multivariable polynomial positivity with control applications
    • Bose N.K., and Modaress A.R. General procedure for multivariable polynomial positivity with control applications. IEEE Trans. Automat. Control 21 (1976) 596-601
    • (1976) IEEE Trans. Automat. Control , vol.21 , pp. 596-601
    • Bose, N.K.1    Modaress, A.R.2
  • 4
    • 0016035949 scopus 로고
    • Tellegon's theorem and multivariable realizability theory
    • Bose N.K., and Newcomb R.W. Tellegon's theorem and multivariable realizability theory. Int. J. Electron. 36 (1974) 417-425
    • (1974) Int. J. Electron. , vol.36 , pp. 417-425
    • Bose, N.K.1    Newcomb, R.W.2
  • 5
    • 0032612381 scopus 로고    scopus 로고
    • High-order contrasts for independent component analysis
    • Cardoso J.F. High-order contrasts for independent component analysis. Neural Comput. 11 (1999) 157-192
    • (1999) Neural Comput. , vol.11 , pp. 157-192
    • Cardoso, J.F.1
  • 7
    • 0028416938 scopus 로고
    • Independent component analysis, a new concept?
    • Comon P. Independent component analysis, a new concept?. Signal Processing 36 (1994) 287-314
    • (1994) Signal Processing , vol.36 , pp. 287-314
    • Comon, P.1
  • 8
    • 0030234706 scopus 로고    scopus 로고
    • Decomposition of quantics in sums of powers of linear forms
    • Comon P., and Mourrain B. Decomposition of quantics in sums of powers of linear forms. Signal Processing 53 (1996) 96-107
    • (1996) Signal Processing , vol.53 , pp. 96-107
    • Comon, P.1    Mourrain, B.2
  • 9
    • 0032186918 scopus 로고    scopus 로고
    • Comments on 'A procedure for the positive definiteness of forms of even-order'
    • Fu M. Comments on 'A procedure for the positive definiteness of forms of even-order'. IEEE Trans. Automat. Control 43 (1998) 1430
    • (1998) IEEE Trans. Automat. Control , vol.43 , pp. 1430
    • Fu, M.1
  • 11
    • 0030127026 scopus 로고    scopus 로고
    • A procedure for the positive definiteness of forms of even-order
    • Hasan M.A., and Hasan A.A. A procedure for the positive definiteness of forms of even-order. IEEE Trans. Automat. Control 41 (1996) 615-617
    • (1996) IEEE Trans. Automat. Control , vol.41 , pp. 615-617
    • Hasan, M.A.1    Hasan, A.A.2
  • 13
    • 0036018642 scopus 로고    scopus 로고
    • On the best rank-1 approximation of higher-order supersymmetric tensors
    • Kofidis E., and Regalia P.A. On the best rank-1 approximation of higher-order supersymmetric tensors. SIAM J. Matrix Anal. Appl. 23 (2002) 863-884
    • (2002) SIAM J. Matrix Anal. Appl. , vol.23 , pp. 863-884
    • Kofidis, E.1    Regalia, P.A.2
  • 14
    • 16244365490 scopus 로고
    • Explicit criterion for the positive definiteness of a general quartic form
    • Ku W.H. Explicit criterion for the positive definiteness of a general quartic form. IEEE Trans. Automat. Control 10 (1965) 372-373
    • (1965) IEEE Trans. Automat. Control , vol.10 , pp. 372-373
    • Ku, W.H.1
  • 16
    • 33750361021 scopus 로고    scopus 로고
    • From matrix to tensor: Multilinear algebra and signal processing
    • McWhirter J. (Ed). Selected papers presented at 4th IMA Int. Conf. on Mathematics in Signal Processing, Oxford University Press, Oxford, UK
    • De Lathauwer L., and De Moor B. From matrix to tensor: Multilinear algebra and signal processing. In: McWhirter J. (Ed). Mathematics in Signal Processing IV. Selected papers presented at 4th IMA Int. Conf. on Mathematics in Signal Processing (1998), Oxford University Press, Oxford, UK 1-15
    • (1998) Mathematics in Signal Processing IV , pp. 1-15
    • De Lathauwer, L.1    De Moor, B.2
  • 17
    • 33846606151 scopus 로고    scopus 로고
    • L.-H. Lim, Singular values and eigenvalues of tensors: A variational approach, Proceedings of the 1st IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), December 13-15, 2005, pp. 129-132
  • 18
    • 84960556527 scopus 로고
    • Some formulae in elimination
    • Macaulay F. Some formulae in elimination. Proc. London Math. Soc. 33 (1902) 3-27
    • (1902) Proc. London Math. Soc. , vol.33 , pp. 3-27
    • Macaulay, F.1
  • 20
    • 33846606794 scopus 로고    scopus 로고
    • G. Ni, L. Qi, F. Wang, A Z-eigenvalue method for positive definiteness identification of quartic forms with three variables, Department of Applied Mathematics, The Hong Kong Polytechnic University, March 2006
  • 21
    • 33846587027 scopus 로고    scopus 로고
    • Q. Ni, L. Qi, F. Wang, An eigenvalue method for the positive definiteness identification problem, Department of Applied Mathematics, The Hong Kong Polytechnic University, June 2005
  • 22
    • 85032751474 scopus 로고
    • Signal processing with higher-order spectra
    • Nikias C.L., and Mendel J.M. Signal processing with higher-order spectra. IEEE Signal Process. Mag. 10 (1993) 10-37
    • (1993) IEEE Signal Process. Mag. , vol.10 , pp. 10-37
    • Nikias, C.L.1    Mendel, J.M.2
  • 23
    • 33846644883 scopus 로고    scopus 로고
    • P.A. Parrilo, Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization, PhD Thesis, California Institute of Technology, May 2000
  • 24
    • 27744582534 scopus 로고    scopus 로고
    • Eigenvalues of a real supersymmetric tensor
    • Qi L. Eigenvalues of a real supersymmetric tensor. J. Symbolic Comput. 40 (2005) 1302-1324
    • (2005) J. Symbolic Comput. , vol.40 , pp. 1302-1324
    • Qi, L.1
  • 25
    • 33846646953 scopus 로고    scopus 로고
    • L. Qi, Rank and eigenvalues of a supersymmetric tensor, the multivariate homogeneous polynomial and the algebraic hypersurface it defines, J. Symbolic Comput., in press
  • 26
    • 33750335770 scopus 로고    scopus 로고
    • Eigenvalues and invariants of tensors
    • Qi L. Eigenvalues and invariants of tensors. J. Math. Anal. Appl. 325 2 (2007) 1363-1377
    • (2007) J. Math. Anal. Appl. , vol.325 , Issue.2 , pp. 1363-1377
    • Qi, L.1
  • 27
    • 0042307364 scopus 로고    scopus 로고
    • Multivariate polynomial minimization and its application in signal processing
    • Qi L., and Teo K.L. Multivariate polynomial minimization and its application in signal processing. J. Global Optim. 46 (2003) 419-433
    • (2003) J. Global Optim. , vol.46 , pp. 419-433
    • Qi, L.1    Teo, K.L.2
  • 30
    • 16244411377 scopus 로고    scopus 로고
    • Comments on 'Explicit criterion for the positive definiteness of a general quartic form'
    • Wang F., and Qi L. Comments on 'Explicit criterion for the positive definiteness of a general quartic form'. IEEE Trans. Automat. Control 50 (2005) 416-418
    • (2005) IEEE Trans. Automat. Control , vol.50 , pp. 416-418
    • Wang, F.1    Qi, L.2
  • 31
    • 0036056838 scopus 로고    scopus 로고
    • Rank-1 approximation of higher-order tensors
    • Zhang T., and Golub G.H. Rank-1 approximation of higher-order tensors. SIAM J. Matrix Anal. Appl. 23 (2001) 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.