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Volumn 45, Issue 3, 2003, Pages 504-519

J-orthogonal matrices: Properties and generation

Author keywords

Exchange operator; Gyration operator; Hyperbolic CS decomposition; Hyperbolic QR factorization; Indefinite least squares problem; Indefinite polar decomposition; J orthogonal matrix; Newton's method; Pivot transform; Principal; Schulz iteration; Sweep operator; Two sided scaling

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING; REGRESSION ANALYSIS;

EID: 0242498756     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036144502414930     Document Type: Article
Times cited : (93)

References (40)
  • 1
    • 0142169408 scopus 로고    scopus 로고
    • Solving the indefinite least squares problem by hyperbolic QR factorization
    • A. Bojanczyk, N. J. Higham, and H. Patel, Solving the indefinite least squares problem by hyperbolic QR factorization, SIAM J. Matrix Anal. Appl., 24 (2003), pp. 914-931.
    • (2003) SIAM J. Matrix Anal. Appl. , vol.24 , pp. 914-931
    • Bojanczyk, A.1    Higham, N.J.2    Patel, H.3
  • 2
    • 0345924583 scopus 로고
    • Existence of the hyperbolic singular value decomposition
    • A. W. Bojanczyk, R. Onn, and A. O. Steinhardt, Existence of the hyperbolic singular value decomposition, Linear Algebra Appl., 185 (1993), pp. 21-30.
    • (1993) Linear Algebra Appl. , vol.185 , pp. 21-30
    • Bojanczyk, A.W.1    Onn, R.2    Steinhardt, A.O.3
  • 4
    • 0039506177 scopus 로고    scopus 로고
    • Polar decompositions in finite dimensional indefinite scalar product spaces: General theory
    • Y. Bolshakov, C. V. M. van der Mee, A. C. M. Ran, B. Reichstein, and L. Rodman, Polar decompositions in finite dimensional indefinite scalar product spaces: General theory, Linear Algebra Appl., 261 (1997), pp. 91-141.
    • (1997) Linear Algebra Appl. , vol.261 , pp. 91-141
    • Bolshakov, Y.1    Van Der Mee, C.V.M.2    Ran, A.C.M.3    Reichstein, B.4    Rodman, L.5
  • 5
    • 0004537774 scopus 로고
    • Eigenvalues of Ax = λBx for real symmetric matrices A and B computed by reduction to a pseudosymmetric form on the HR process
    • M. A. Brebner and J. Grad, Eigenvalues of Ax = λBx for real symmetric matrices A and B computed by reduction to a pseudosymmetric form on the HR process, Linear Algebra Appl., 43 (1982), pp. 99-118.
    • (1982) Linear Algebra Appl. , vol.43 , pp. 99-118
    • Brebner, M.A.1    Grad, J.2
  • 6
    • 0001423566 scopus 로고
    • An analysis of the HR algorithm for computing the eigenvalues of a matrix
    • A. Bunse-Gerstner, An analysis of the HR algorithm for computing the eigenvalues of a matrix, Linear Algebra Appl., 35 (1981), pp. 155-173.
    • (1981) Linear Algebra Appl. , vol.35 , pp. 155-173
    • Bunse-Gerstner, A.1
  • 7
    • 85039608539 scopus 로고    scopus 로고
    • Computing the square root and logarithm of a real P-orthogonal matrix
    • to appear
    • J. R. Cardoso, C. S. Kenney, and F. Silva Leite, Computing the square root and logarithm of a real P-orthogonal matrix, Appl. Numer. Math., to appear.
    • Appl. Numer. Math.
    • Cardoso, J.R.1    Kenney, C.S.2    Silva Leite, F.3
  • 8
    • 0242598267 scopus 로고    scopus 로고
    • Extending results from orthogonal matrices to the class of P-orthogonal matrices
    • manuscript
    • J. R. Cardoso and F. Silva Leite, Extending Results from Orthogonal Matrices to the Class of P-Orthogonal Matrices, manuscript, 2002.
    • (2002)
    • Cardoso, J.R.1    Silva Leite, F.2
  • 9
    • 0032216887 scopus 로고    scopus 로고
    • A stable and efficient algorithm for the indefinite linear least-squares problem
    • S. Chandrasekaran, M. Gu, and A. H. Sayed, A stable and efficient algorithm for the indefinite linear least-squares problem, SIAM J. Matrix Anal. Appl., 20 (1998), pp. 354-362.
    • (1998) SIAM J. Matrix Anal. Appl. , vol.20 , pp. 354-362
    • Chandrasekaran, S.1    Gu, M.2    Sayed, A.H.3
  • 10
  • 11
    • 84968511031 scopus 로고
    • Some metric inequalities in the space of matrices
    • K. Fan and A. J. Hoffman, Some metric inequalities in the space of matrices, Proc. Amer. Math. Soc., 6 (1955), pp. 111-116.
    • (1955) Proc. Amer. Math. Soc. , vol.6 , pp. 111-116
    • Fan, K.1    Hoffman, A.J.2
  • 13
    • 84947680781 scopus 로고
    • A tutorial on the SWEEP operator
    • J. H. Goodnight, A tutorial on the SWEEP operator, Amer. Statist., 33 (1979), pp. 149-158.
    • (1979) Amer. Statist. , vol.33 , pp. 149-158
    • Goodnight, J.H.1
  • 14
    • 27544508073 scopus 로고    scopus 로고
    • Model reduction of state space systems via an implicitly restarted Lanczos method
    • E. J. Grimme, D. C. Sorensen, and P. Van Dooren, Model reduction of state space systems via an implicitly restarted Lanczos method, Numer. Algorithms, 12 (1996), pp. 1-31.
    • (1996) Numer. Algorithms , vol.12 , pp. 1-31
    • Grimme, E.J.1    Sorensen, D.C.2    Van Dooren, P.3
  • 15
    • 0001692403 scopus 로고
    • Computing the polar decomposition - With applications
    • N. J. Higham, Computing the polar decomposition - with applications, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 1160-1174.
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 1160-1174
    • Higham, N.J.1
  • 16
    • 0001485725 scopus 로고
    • Computing real square roots of a real matrix
    • N. J. Higham, Computing real square roots of a real matrix, Linear Algebra Appl., 88/89 (1987), pp. 405-430.
    • (1987) Linear Algebra Appl. , vol.88-89 , pp. 405-430
    • Higham, N.J.1
  • 17
    • 0001930482 scopus 로고
    • Matrix nearness problems and applications
    • M. J. C. Gover and S. Barnett, eds., Oxford University Press, Oxford
    • N. J. Higham, Matrix nearness problems and applications, in Applications of Matrix Theory, M. J. C. Gover and S. Barnett, eds., Oxford University Press, Oxford, 1989, pp. 1-27.
    • (1989) Applications of Matrix Theory , pp. 1-27
    • Higham, N.J.1
  • 18
    • 21944447246 scopus 로고    scopus 로고
    • Stable iterations for the matrix square root
    • N. J. Higham, Stable iterations for the matrix square root, Numer. Algorithms, 15 (1997), pp. 227-242.
    • (1997) Numer. Algorithms , vol.15 , pp. 227-242
    • Higham, N.J.1
  • 20
  • 21
    • 0004151494 scopus 로고
    • Cambridge University Press, Cambridge, England
    • R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, England, 1985.
    • (1985) Matrix Analysis
    • Horn, R.A.1    Johnson, C.R.2
  • 22
    • 0001246152 scopus 로고
    • Rational iterative methods for the matrix sign function
    • C. Kenney and A. J. Laub, Rational iterative methods for the matrix sign function, SIAM J. Matrix Anal. Appl., 12 (1991), pp. 273-291.
    • (1991) SIAM J. Matrix Anal. Appl. , vol.12 , pp. 273-291
    • Kenney, C.1    Laub, A.J.2
  • 23
    • 0000204992 scopus 로고
    • On scaling Newton's method for polar decomposition and the matrix sign function
    • C. Kenney and A. J. Laub, On scaling Newton's method for polar decomposition and the matrix sign function, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 688-706.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 688-706
    • Kenney, C.1    Laub, A.J.2
  • 24
    • 85039612853 scopus 로고    scopus 로고
    • G-reflectors: Analogues of householder transformations in scalar product spaces
    • to appear
    • D. S. Mackey, N. Mackey, and F. Tisseur, G-reflectors: Analogues of Householder transformations in scalar product spaces, Linear Algebra Appl., to appear.
    • Linear Algebra Appl.
    • Mackey, D.S.1    Mackey, N.2    Tisseur, F.3
  • 25
    • 85039613709 scopus 로고    scopus 로고
    • Structured factorizations for structured matrices
    • Numerical analysis report, Manchester Centre for Computational Mathematics, Manchester, England, in preparation
    • D. S. Mackey, N. Mackey, and F. Tisseur, Structured Factorizations for Structured Matrices, Numerical analysis report, Manchester Centre for Computational Mathematics, Manchester, England, in preparation.
    • Mackey, D.S.1    Mackey, N.2    Tisseur, F.3
  • 27
    • 0037555939 scopus 로고    scopus 로고
    • Structured Jordan canonical forms for structured matrices that are Hermitian, skew Hermitian or unitary with respect to indefinite inner products
    • V. Mehrmann and H. Xu, Structured Jordan canonical forms for structured matrices that are Hermitian, skew Hermitian or unitary with respect to indefinite inner products, Electron. J. Linear Algebra, 5, (1999), pp. 67-103.
    • (1999) Electron. J. Linear Algebra , vol.5 , pp. 67-103
    • Mehrmann, V.1    Xu, H.2
  • 28
    • 7544236723 scopus 로고
    • History and generality of the CS decomposition
    • C. C. Paige and M. Wei, History and generality of the CS decomposition, Linear Algebra Appl., 208/209 (1994), pp. 303-326.
    • (1994) Linear Algebra Appl. , vol.208-209 , pp. 303-326
    • Paige, C.C.1    Wei, M.2
  • 29
    • 0000882117 scopus 로고
    • Least squares modifications with inverse factorizations: Parallel implications
    • C.-T. Pan and R. J. Plemmons, Least squares modifications with inverse factorizations: Parallel implications, J. Comput. Appl. Math., 27 (1989), pp. 109-127.
    • (1989) J. Comput. Appl. Math. , vol.27 , pp. 109-127
    • Pan, C.-T.1    Plemmons, R.J.2
  • 30
    • 0000338056 scopus 로고
    • The multiplicative structure of J-contractive matrix functions
    • V. P. Potapov, The multiplicative structure of J-contractive matrix functions, Amer. Math. Soc. Transl. (2), 15 (1960), pp. 131-243.
    • (1960) Amer. Math. Soc. Transl. (2) , vol.15 , pp. 131-243
    • Potapov, V.P.1
  • 31
    • 84979324358 scopus 로고
    • Iterative Berechnung der reziproken Matrix
    • G. Schulz, Iterative Berechnung der reziproken Matrix, Z. Angew. Math. Mech., 13 (1933), pp. 57-59.
    • (1933) Z. Angew. Math. Mech. , vol.13 , pp. 57-59
    • Schulz, G.1
  • 32
    • 85039608452 scopus 로고    scopus 로고
    • A fast method for variable selection in the general linear model
    • Technical Report CUED/F-INFENG/TR 288, Signal Processing and Communications Laboratory, Cambridge University, Cambridge, England
    • J. A. Stark and W. J. Fitzgerald, A Fast Method for Variable Selection in the General Linear Model, Technical Report CUED/F-INFENG/TR 288, Signal Processing and Communications Laboratory, Cambridge University, Cambridge, England, 1997.
    • (1997)
    • Stark, J.A.1    Fitzgerald, W.J.2
  • 33
    • 0000485973 scopus 로고
    • The efficient generation of random orthogonal matrices with an application to condition estimators
    • G. W. Stewart, The efficient generation of random orthogonal matrices with an application to condition estimators, SIAM J. Numer. Anal., 17 (1980), pp. 403-409.
    • (1980) SIAM J. Numer. Anal. , vol.17 , pp. 403-409
    • Stewart, G.W.1
  • 36
    • 0032339289 scopus 로고    scopus 로고
    • On hyperbolic triangularization: Stability and pivoting
    • M. Stewart and G. W. Stewart, On hyperbolic triangularization: Stability and pivoting, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 847-860.
    • (1998) SIAM J. Matrix Anal. Appl. , vol.19 , pp. 847-860
    • Stewart, M.1    Stewart, G.W.2
  • 37
    • 26744464408 scopus 로고    scopus 로고
    • On the factorization of hyperbolic and unitary transformations into rotations
    • manuscript
    • M. Stewart and P. Van Dooren, On the Factorization of Hyperbolic and Unitary Transformations into Rotations, manuscript, 2002.
    • (2002)
    • Stewart, M.1    Van Dooren, P.2
  • 38
    • 0242682028 scopus 로고    scopus 로고
    • Tridiagonal-diagonal reduction of symmetric indefinite pairs
    • Numerical Analysis Report 409, Manchester Centre for Computational Mathematics, Manchester, England
    • F. Tisseur, Tridiagonal-Diagonal Reduction of Symmetric Indefinite Pairs, Numerical Analysis Report 409, Manchester Centre for Computational Mathematics, Manchester, England, 2002.
    • (2002)
    • Tisseur, F.1
  • 39
    • 0034422799 scopus 로고    scopus 로고
    • Principal pivot transforms: Properties and applications
    • M. J. Tsatsomeros, Principal pivot transforms: Properties and applications, Linear Algebra Appl., 307 (2000), pp. 151-165.
    • (2000) Linear Algebra Appl. , vol.307 , pp. 151-165
    • Tsatsomeros, M.J.1
  • 40
    • 21144467676 scopus 로고
    • A Jacobi eigenreduction algorithm for definite matrix pairs
    • K. Veselić, A Jacobi eigenreduction algorithm for definite matrix pairs, Numer. Math., 64 (1993), pp. 241-269.
    • (1993) Numer. Math. , vol.64 , pp. 241-269
    • Veselić, K.1


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