메뉴 건너뛰기




Volumn 53, Issue 5, 2008, Pages 1096-1107

An eigenvalue method for testing positive definiteness of a multivariate form

Author keywords

Eigenvalue method; Positive definiteness; Supersymmetric tensor; Symmetric hyperdeterminant

Indexed keywords

AUTOMATION; CONTROL THEORY; INFORMATION THEORY; SYSTEM STABILITY; TENSORS; THREE DIMENSIONAL;

EID: 51749116732     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.923679     Document Type: Article
Times cited : (125)

References (28)
  • 1
    • 0016472847 scopus 로고
    • Output feedback stabilization and related problems-solutions via decision methods
    • Dec
    • B. D. Anderson, N. K. Bose, and E. I. Jury, "Output feedback stabilization and related problems-solutions via decision methods," IEEE Trans. Autom. Control, vol. AC-20, no. 6, pp. 55-66, Dec. 1975.
    • (1975) IEEE Trans. Autom. Control , vol.AC-20 , Issue.6 , pp. 55-66
    • Anderson, B.D.1    Bose, N.K.2    Jury, E.I.3
  • 2
    • 0016036975 scopus 로고
    • Stability of multidimensional digital filters
    • Mar
    • B. D. Anderson and E. I. Jury, "Stability of multidimensional digital filters," IEEE Trans. Circuits Syst., vol. CAS-21, no. 2, pp. 300-304, Mar. 1974.
    • (1974) IEEE Trans. Circuits Syst , vol.CAS-21 , Issue.2 , pp. 300-304
    • Anderson, B.D.1    Jury, E.I.2
  • 3
    • 0000197849 scopus 로고    scopus 로고
    • Multivariate Bezoutians, Kronecker symbol and Eisenbud-Levine formula, in algorithms in algebraic geometry and applications
    • E. Becker, J. Cardinal, M. Roy, and Z. Szafraniec, "Multivariate Bezoutians, Kronecker symbol and Eisenbud-Levine formula, in algorithms in algebraic geometry and applications," Progress Math., vol. 143, pp. 79-104, 1996.
    • (1996) Progress Math , vol.143 , pp. 79-104
    • Becker, E.1    Cardinal, J.2    Roy, M.3    Szafraniec, Z.4
  • 4
    • 84968468488 scopus 로고
    • Solution of Vandermonde systems of equations
    • A. Björck and V. Pereyra, "Solution of Vandermonde systems of equations," Math. Comput., vol. 24, pp. 893-903, 1970.
    • (1970) Math. Comput , vol.24 , pp. 893-903
    • Björck, A.1    Pereyra, V.2
  • 6
    • 0016117528 scopus 로고
    • Algorithm for stability test of multidimensional filters
    • Oct
    • N. K. Bose and P. S. Kamat, "Algorithm for stability test of multidimensional filters," IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-22, no. 5, pp. 307-314, Oct. 1974.
    • (1974) IEEE Trans. Acoust., Speech, Signal Process , vol.ASSP-22 , Issue.5 , pp. 307-314
    • Bose, N.K.1    Kamat, P.S.2
  • 7
    • 0001559061 scopus 로고
    • A quadratic form representation of polynomials of several variables and its applications
    • Aug
    • N. K. Bose and C. C. Li, "A quadratic form representation of polynomials of several variables and its applications," IEEE Trans. Autom. Control, vol. AC-13, no. 4, pp. 447-448, Aug. 1968.
    • (1968) IEEE Trans. Autom. Control , vol.AC-13 , Issue.4 , pp. 447-448
    • Bose, N.K.1    Li, C.C.2
  • 8
    • 0017012938 scopus 로고
    • General procedure for multivariable polynomial positivity with control applications
    • Oct
    • N. K. Bose and A. R. Modarressi, "General procedure for multivariable polynomial positivity with control applications," IEEE Trans. Autom. Control, vol. AC-21, no. 5, pp. 696-701, Oct. 1976.
    • (1976) IEEE Trans. Autom. Control , vol.AC-21 , Issue.5 , pp. 696-701
    • Bose, N.K.1    Modarressi, A.R.2
  • 9
    • 0016035949 scopus 로고
    • Tellegon's theorem and multivariable realizability theory
    • N. K. Bose and R. W. Newcomb, "Tellegon's theorem and multivariable realizability theory," Int. J. Electron., vol. 36, pp. 417-425, 1974.
    • (1974) Int. J. Electron , vol.36 , pp. 417-425
    • Bose, N.K.1    Newcomb, R.W.2
  • 12
    • 0002569434 scopus 로고    scopus 로고
    • Explicit formulas for the multi-variate resultant
    • C. D'Andrea and A. Dickenstein, "Explicit formulas for the multi-variate resultant," J. Pure Appl. Algebra, vol. 164, pp. 59-86, 2001.
    • (2001) J. Pure Appl. Algebra , vol.164 , pp. 59-86
    • D'Andrea, C.1    Dickenstein, A.2
  • 13
    • 0032186918 scopus 로고    scopus 로고
    • Comments on 'A procedure for the positive definiteness of forms of even-order'
    • Oct
    • M. Fu, "Comments on 'A procedure for the positive definiteness of forms of even-order'," IEEE Trans. Autom. Control, vol. AC-43, no. 10, p. 1430, Oct. 1998.
    • (1998) IEEE Trans. Autom. Control , vol.AC-43 , Issue.10 , pp. 1430
    • Fu, M.1
  • 15
    • 0030127026 scopus 로고    scopus 로고
    • A procedure for the positive definiteness of forms of even-order
    • Oct
    • M. A. Hasan and A. A. Hasan, "A procedure for the positive definiteness of forms of even-order," IEEE Trans. Autom. Control, vol. AC-41, no. 4, pp. 615-617, Oct. 1996.
    • (1996) IEEE Trans. Autom. Control , vol.AC-41 , Issue.4 , pp. 615-617
    • Hasan, M.A.1    Hasan, A.A.2
  • 18
    • 0015632446 scopus 로고
    • Stability criterion for N-dimensional digital filters
    • Jun
    • J. H. Justice and J. L. Shanks, "Stability criterion for N-dimensional digital filters," IEEE Trans. Autom. Control, vol. AC-18, no. 3, pp. 284-286, Jun. 1973.
    • (1973) IEEE Trans. Autom. Control , vol.AC-18 , Issue.3 , pp. 284-286
    • Justice, J.H.1    Shanks, J.L.2
  • 19
    • 0036018642 scopus 로고    scopus 로고
    • On the best rank-1 approximation of higher-order supersymmetric tensors
    • E. Kofidis and P. A. Regalia, "On the best rank-1 approximation of higher-order supersymmetric tensors," SIAM J. Matrix Anal. Appl., vol. 23, pp. 863-884, 2002.
    • (2002) SIAM J. Matrix Anal. Appl , vol.23 , pp. 863-884
    • Kofidis, E.1    Regalia, P.A.2
  • 21
    • 16244365490 scopus 로고
    • Explicit criterion for the positive definiteness of a general quartic form
    • Jul
    • W. H. Ku, "Explicit criterion for the positive definiteness of a general quartic form," IEEE Trans. Autom. Control, vol. AC-10, no. 3, pp. 372-373, Jul. 1965.
    • (1965) IEEE Trans. Autom. Control , vol.AC-10 , Issue.3 , pp. 372-373
    • Ku, W.H.1
  • 22
    • 84960556527 scopus 로고
    • Some formulae in elimination
    • F. Macaulay, "Some formulae in elimination," Proc. London Math. Soc., vol. 33, pp. 3-27, 1902.
    • (1902) Proc. London Math. Soc , vol.33 , pp. 3-27
    • Macaulay, F.1
  • 23
    • 33846621614 scopus 로고    scopus 로고
    • The degree of the e-characteristic polynomial of an even order tensor
    • G. Ni, L. Qi, F. Wang, and Y. Wang, "The degree of the e-characteristic polynomial of an even order tensor," J. Math. Anal. Appl., vol. 329, pp. 1218-1229, 2007.
    • (2007) J. Math. Anal. Appl , vol.329 , pp. 1218-1229
    • Ni, G.1    Qi, L.2    Wang, F.3    Wang, Y.4
  • 24
    • 27744582534 scopus 로고    scopus 로고
    • Eigenvalues of a real supersymmetric tensor
    • L. Qi, "Eigenvalues of a real supersymmetric tensor," J. Symbol. Comput., vol. 40, pp. 1302-1324, 2005.
    • (2005) J. Symbol. Comput , vol.40 , pp. 1302-1324
    • Qi, L.1
  • 25
    • 33750796673 scopus 로고    scopus 로고
    • Rank and eigenvalues of a supersymmetric tensor, the multi-variate homogeneous polynomial and the algebraic hypersurface it defines
    • L. Qi, "Rank and eigenvalues of a supersymmetric tensor, the multi-variate homogeneous polynomial and the algebraic hypersurface it defines," J. Symbol. Comput., vol. 41, pp. 1309-1327, 2006.
    • (2006) J. Symbol. Comput , vol.41 , pp. 1309-1327
    • Qi, L.1
  • 26
    • 33750335770 scopus 로고    scopus 로고
    • Eigenvalues and invariants of tensors
    • L. Qi, "Eigenvalues and invariants of tensors," J. Math. Anal. Appl., vol. 325, pp. 1363-1377, 2007.
    • (2007) J. Math. Anal. Appl , vol.325 , pp. 1363-1377
    • Qi, L.1
  • 27
    • 51749109442 scopus 로고    scopus 로고
    • B. Sturmfels, Solving Systems of Polynomial Equations. Providence, RI: AMS Bookstore, 2002.
    • B. Sturmfels, Solving Systems of Polynomial Equations. Providence, RI: AMS Bookstore, 2002.
  • 28
    • 16244411377 scopus 로고    scopus 로고
    • Comments on 'Explicit criterion for the positive definiteness of a general quartic form'
    • Mar
    • F. Wang and L. Qi, "Comments on 'Explicit criterion for the positive definiteness of a general quartic form'," IEEE Trans. Autom. Control vol. 50, no. 3, pp. 416-418, Mar. 2005.
    • (2005) IEEE Trans. Autom. Control , vol.50 , Issue.3 , pp. 416-418
    • Wang, F.1    Qi, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.