메뉴 건너뛰기




Volumn 437, Issue 11, 2012, Pages 2793-2812

On the generalized reflexive and anti-reflexive solutions to a system of matrix equations

Author keywords

Generalized anti reflexive matrix; Generalized reflexive matrix; Iterative algorithm; System of matrix equations

Indexed keywords

CONJUGATE GRADIENT LEAST SQUARES; ITERATIVE ALGORITHM; LEAST FROBENIUS NORMS; LINEAR OPERATORS; LYAPUNOV MATRIX EQUATIONS; M-MATRICES; MATRIX EQUATIONS; MATRIX PAIRS; N-MATRIX; NUMERICAL EXAMPLE; OPTIMAL APPROXIMATION; REFLECTION MATRIX; REFLEXIVE MATRIX;

EID: 84865699780     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2012.07.004     Document Type: Article
Times cited : (44)

References (51)
  • 3
    • 0032340222 scopus 로고    scopus 로고
    • Generalized reflexive matrices: Special properties and applications
    • H.C. Chen Generalized reflexive matrices: special properties and applications SIAM J. Matrix Anal. Appl. 19 1998 140 153
    • (1998) SIAM J. Matrix Anal. Appl. , vol.19 , pp. 140-153
    • Chen, H.C.1
  • 4
    • 0023565792 scopus 로고
    • Numerical linear algebra algorithms on the ceder system
    • A.K. Noor (Ed.) AMD-vol. 86 The American Society of Mechanical Engineers
    • H.C. Chen, A. Sameh, Numerical linear algebra algorithms on the ceder system, in: A.K. Noor (Ed.), Parrallel computations and their impact on mechanics, AMD-vol. 86, The American Society of Mechanical Engineers, 1987, pp. 101-125.
    • (1987) Parrallel Computations and Their Impact on Mechanics , pp. 101-125
    • Chen, H.C.1    Sameh, A.2
  • 5
    • 0040731746 scopus 로고
    • CSRD Teach, report 754, Center for Supercomputing Research and Development, University of Illinois, Urbana, IL
    • H.C. Chen, The SAS domain decomposition method for structural analysis, CSRD Teach, report 754, Center for Supercomputing Research and Development, University of Illinois, Urbana, IL, 1988.
    • (1988) The SAS Domain Decomposition Method for Structural Analysis
    • Chen, H.C.1
  • 7
    • 77956363397 scopus 로고    scopus 로고
    • The reflexive and anti-reflexive solutions of a linear matrix equation and systems of matrix equations
    • M. Dehghan, and M. Hajarian The reflexive and anti-reflexive solutions of a linear matrix equation and systems of matrix equations Rocky Mountain J. Math. 40 2010 1 23
    • (2010) Rocky Mountain J. Math. , vol.40 , pp. 1-23
    • Dehghan, M.1    Hajarian, M.2
  • 8
    • 84858601388 scopus 로고    scopus 로고
    • On the generalized bisymmetric and skew-symmetric solutions of the system of generalized Sylvester matrix equations
    • M. Dehghan, and M. Hajarian On the generalized bisymmetric and skew-symmetric solutions of the system of generalized Sylvester matrix equations Linear Multilinear Algebra 59 2011 1281 1309
    • (2011) Linear Multilinear Algebra , vol.59 , pp. 1281-1309
    • Dehghan, M.1    Hajarian, M.2
  • 9
    • 79960921037 scopus 로고    scopus 로고
    • The generalized centro-symmetric and least squares generalized centro-symmetric solutions of the matrix equation AYB + CY T D = e
    • M. Hajarian, and M. Dehghan The generalized centro-symmetric and least squares generalized centro-symmetric solutions of the matrix equation AYB + CY T D = E Math. Meth. Appl. Sci. 34 2011 1562 1579
    • (2011) Math. Meth. Appl. Sci. , vol.34 , pp. 1562-1579
    • Hajarian, M.1    Dehghan, M.2
  • 10
    • 79951705395 scopus 로고    scopus 로고
    • Solving the generalized Sylvester matrix equation Solving the generalized Sylvester matrix equation ∑ i = 1 p A i XB i + ∑ j = 1 q C j YD j = e over reflexive and anti-reflexive matrices
    • M. Dehghan, and M. Hajarian Solving the generalized Sylvester matrix equation ∑ i = 1 p A i XB i + ∑ j = 1 q C j YD j = E over reflexive and anti-reflexive matrices Int. J. Contr. Automat. Syst. 9 2011 118 124
    • (2011) Int. J. Contr. Automat. Syst. , vol.9 , pp. 118-124
    • Dehghan, M.1    Hajarian, M.2
  • 11
    • 79953198577 scopus 로고    scopus 로고
    • Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations
    • M. Dehghan, and M. Hajarian Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations Appl. Math. Modell. 35 2011 3285 3300
    • (2011) Appl. Math. Modell. , vol.35 , pp. 3285-3300
    • Dehghan, M.1    Hajarian, M.2
  • 12
    • 78650509563 scopus 로고    scopus 로고
    • Two algorithms for the Hermitian reflexive and skew-Hermitian solutions of Sylvester matrix equations
    • M. Dehghan, and M. Hajarian Two algorithms for the Hermitian reflexive and skew-Hermitian solutions of Sylvester matrix equations Appl. Math. Lett. 24 2011 444 449
    • (2011) Appl. Math. Lett. , vol.24 , pp. 444-449
    • Dehghan, M.1    Hajarian, M.2
  • 13
    • 84858613324 scopus 로고    scopus 로고
    • The (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations the (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A 1 XB 1 = C 1 and A 2 XB 2 = C 2
    • M. Dehghan, and M. Hajarian The (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A 1 XB 1 = C 1 and A 2 XB 2 = C 2 Bull. Iranian Math. Soc. 37 2011 269 279
    • (2011) Bull. Iranian Math. Soc. , vol.37 , pp. 269-279
    • Dehghan, M.1    Hajarian, M.2
  • 14
    • 82255169141 scopus 로고    scopus 로고
    • SSHI methods for solving general linear matrix equations
    • M. Dehghan, and M. Hajarian SSHI methods for solving general linear matrix equations Eng. Comput. 28 2012 1028 1043
    • (2012) Eng. Comput. , vol.28 , pp. 1028-1043
    • Dehghan, M.1    Hajarian, M.2
  • 15
    • 84863700837 scopus 로고    scopus 로고
    • The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices
    • M. Dehghan, and M. Hajarian The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices Int. J. Syst. Sci. 43 2012 1580 1590
    • (2012) Int. J. Syst. Sci. , vol.43 , pp. 1580-1590
    • Dehghan, M.1    Hajarian, M.2
  • 16
    • 26244448321 scopus 로고    scopus 로고
    • Gradient based iterative algorithms for solving a class of matrix equations
    • F. Ding, and T. Chen Gradient based iterative algorithms for solving a class of matrix equations IEEE Trans. Autom. Contr. 50 2005 1216 1221
    • (2005) IEEE Trans. Autom. Contr. , vol.50 , pp. 1216-1221
    • Ding, F.1    Chen, T.2
  • 17
    • 22144434326 scopus 로고    scopus 로고
    • Hierarchical gradient-based identification of multivariable discrete-time systems
    • F. Ding, and T. Chen Hierarchical gradient-based identification of multivariable discrete-time systems Automatica 41 2005 315 325
    • (2005) Automatica , vol.41 , pp. 315-325
    • Ding, F.1    Chen, T.2
  • 18
    • 10444247504 scopus 로고    scopus 로고
    • Iterative least squares solutions of coupled Sylvester matrix equations
    • F. Ding, and T. Chen Iterative least squares solutions of coupled Sylvester matrix equations Syst. Contr. Lett. 54 2005 95 107
    • (2005) Syst. Contr. Lett. , vol.54 , pp. 95-107
    • Ding, F.1    Chen, T.2
  • 19
    • 16244397443 scopus 로고    scopus 로고
    • Hierarchical least squares identification methods for multivariable systems
    • F. Ding, and T. Chen Hierarchical least squares identification methods for multivariable systems IEEE Trans. Autom. Contr. 50 2005 397 402
    • (2005) IEEE Trans. Autom. Contr. , vol.50 , pp. 397-402
    • Ding, F.1    Chen, T.2
  • 20
    • 33751185751 scopus 로고    scopus 로고
    • On iterative solutions of general coupled matrix equations
    • F. Ding, and T. Chen On iterative solutions of general coupled matrix equations SIAM J. Contr. Optim. 44 2006 2269 2284
    • (2006) SIAM J. Contr. Optim. , vol.44 , pp. 2269-2284
    • Ding, F.1    Chen, T.2
  • 21
    • 38949156204 scopus 로고    scopus 로고
    • Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle
    • F. Ding, P.X. Liu, and J. Ding Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle Appl. Math. Comput. 197 2008 41 50
    • (2008) Appl. Math. Comput. , vol.197 , pp. 41-50
    • Ding, F.1    Liu, P.X.2    Ding, J.3
  • 22
    • 10644221060 scopus 로고    scopus 로고
    • The solution to the matrix equation the solution to the matrix equation AV + BW + EVJ + R
    • G.R. Duan The solution to the matrix equation AV + BW + EVJ + R Appl. Math. Lett. 17 2004 1197 1202
    • (2004) Appl. Math. Lett. , vol.17 , pp. 1197-1202
    • Duan, G.R.1
  • 24
    • 0025421966 scopus 로고
    • Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy-A survey and some new results
    • P.M. Frank Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy-a survey and some new results Automatica 26 1990 459 474
    • (1990) Automatica , vol.26 , pp. 459-474
    • Frank, P.M.1
  • 25
    • 0018721357 scopus 로고
    • A Hessenberg-Schur method for the matrix problem A Hessenberg-Schur method for the matrix problem AX + XB = C
    • G.H. Golub, S. Nash, and C.F. Van Loan A Hessenberg-Schur method for the matrix problem AX + XB = C IEEE Trans. Auto. Contr. 24 1979 909 913
    • (1979) IEEE Trans. Auto. Contr. , vol.24 , pp. 909-913
    • Golub, G.H.1    Nash, S.2    Van Loan, C.F.3
  • 26
    • 0000135303 scopus 로고
    • Methods of conjugate gradients for solving linear systems
    • M.R. Hestenes, and E.L. Stiefel Methods of conjugate gradients for solving linear systems J. Natl. Bur. Stand 49 1952 409 436
    • (1952) J. Natl. Bur. Stand , vol.49 , pp. 409-436
    • Hestenes, M.R.1    Stiefel, E.L.2
  • 29
    • 0040773836 scopus 로고
    • Solution of the equation Solution of the equation AX - XB = C by inversion of an M × M or N × N matrix
    • A. Jameson Solution of the equation AX - XB = C by inversion of an M × M or N × N matrix SIAM J. Appl. Math. 16 1968 1020 1023
    • (1968) SIAM J. Appl. Math. , vol.16 , pp. 1020-1023
    • Jameson, A.1
  • 30
    • 34247229524 scopus 로고    scopus 로고
    • On solutions of the matrix equations on solutions of the matrix equations X - AXB = C and X - A X B = C
    • T. Jiang, and M. Wei On solutions of the matrix equations X - AXB = C and X - A X B = C Linear Algebra Appl. 367 2003 429 436
    • (2003) Linear Algebra Appl. , vol.367 , pp. 429-436
    • Jiang, T.1    Wei, M.2
  • 31
    • 0039943513 scopus 로고
    • LSQR: An algorithm for sparse linear equations and sparse least squares
    • C.C. Paige, and M.A. Saunders LSQR: an algorithm for sparse linear equations and sparse least squares ACM Trans. Math. Softw. 8 1982 43 71
    • (1982) ACM Trans. Math. Softw. , vol.8 , pp. 43-71
    • Paige, C.C.1    Saunders, M.A.2
  • 32
    • 35349018439 scopus 로고    scopus 로고
    • The solution to matrix equation the solution to matrix equation AX + X T C = B
    • F. Piao, Q. Zhang, and Z. Wang The solution to matrix equation AX + X T C = B J. Franklin Inst. 344 2007 1056 1062
    • (2007) J. Franklin Inst. , vol.344 , pp. 1056-1062
    • Piao, F.1    Zhang, Q.2    Wang, Z.3
  • 33
    • 2342617534 scopus 로고    scopus 로고
    • A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
    • Q.W. Wang A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity Linear Algebra Appl. 384 2004 43 54
    • (2004) Linear Algebra Appl. , vol.384 , pp. 43-54
    • Wang, Q.W.1
  • 34
    • 58349094506 scopus 로고    scopus 로고
    • Ranks and the least-norm of the general solution to a system of quaternion matrix equations
    • Q.W. Wang, and C.K. Li Ranks and the least-norm of the general solution to a system of quaternion matrix equations Linear Algebra Appl. 430 2009 1626 1640
    • (2009) Linear Algebra Appl. , vol.430 , pp. 1626-1640
    • Wang, Q.W.1    Li, C.K.2
  • 35
    • 40149106637 scopus 로고    scopus 로고
    • The common solution to six quaternion matrix equations with applications
    • Q.W. Wang, H.X. Chang, and Q. Ning The common solution to six quaternion matrix equations with applications Appl. Math. Comput. 198 2008 209 226
    • (2008) Appl. Math. Comput. , vol.198 , pp. 209-226
    • Wang, Q.W.1    Chang, H.X.2    Ning, Q.3
  • 36
    • 40849138243 scopus 로고    scopus 로고
    • The reflexive re-nonnegative definite solution to a quaternion matrix equation
    • Q.W. Wang, and F. Zhang The reflexive re-nonnegative definite solution to a quaternion matrix equation Electron. J. Linear Algebra 17 2008 88 101
    • (2008) Electron. J. Linear Algebra , vol.17 , pp. 88-101
    • Wang, Q.W.1    Zhang, F.2
  • 37
    • 48849100393 scopus 로고    scopus 로고
    • On solutions to the quaternion matrix equation on solutions to the quaternion matrix equation AXB + CYD = e
    • Q.W. Wang, H.S. Zhang, and S.W. Yu On solutions to the quaternion matrix equation AXB + CYD = E Electron. J. Linear Algebra 17 2008 343 358
    • (2008) Electron. J. Linear Algebra , vol.17 , pp. 343-358
    • Wang, Q.W.1    Zhang, H.S.2    Yu, S.W.3
  • 38
    • 70349826930 scopus 로고    scopus 로고
    • A system of real quaternion matrix equations with applications
    • Q.W. Wang, J.W. Woude, and H.X. Chang A system of real quaternion matrix equations with applications Linear Algebra Appl. 431 2009 2291 2303
    • (2009) Linear Algebra Appl. , vol.431 , pp. 2291-2303
    • Wang, Q.W.1    Woude, J.W.2    Chang, H.X.3
  • 39
    • 58349094506 scopus 로고    scopus 로고
    • Ranks and the least-norm of the general solution to a system of quaternion matrix equations
    • Q.W. Wang, and C.K. Li Ranks and the least-norm of the general solution to a system of quaternion matrix equations Linear Algebra Appl. 430 2009 1626 1640
    • (2009) Linear Algebra Appl. , vol.430 , pp. 1626-1640
    • Wang, Q.W.1    Li, C.K.2
  • 40
    • 68749110971 scopus 로고    scopus 로고
    • Gradient based iterative solutions for general linear matrix equations
    • L. Xie, J. Ding, and F. Ding Gradient based iterative solutions for general linear matrix equations Comput. Math. Appl. 58 2009 1441 1448
    • (2009) Comput. Math. Appl. , vol.58 , pp. 1441-1448
    • Xie, L.1    Ding, J.2    Ding, F.3
  • 41
    • 0030492597 scopus 로고    scopus 로고
    • On approximation problems with zero-trace matrices
    • K. Ziȩtak On approximation problems with zero-trace matrices Linear Algebra Appl. 247 1996 169 183
    • (1996) Linear Algebra Appl. , vol.247 , pp. 169-183
    • Ziȩtak, K.1
  • 42
    • 43049176217 scopus 로고    scopus 로고
    • Linear restriction problem of Hermitian reflexive matrices and its approximation
    • L. Zhao, X. Hu, and L. Zhang Linear restriction problem of Hermitian reflexive matrices and its approximation Appl. Math. Comput. 200 2008 341 351
    • (2008) Appl. Math. Comput. , vol.200 , pp. 341-351
    • Zhao, L.1    Hu, X.2    Zhang, L.3
  • 43
    • 30844444393 scopus 로고    scopus 로고
    • A new solution to the generalized Sylvester matrix equation A new solution to the generalized Sylvester matrix equation AV - EVF = BW
    • B. Zhou, and G.R. Duan A new solution to the generalized Sylvester matrix equation AV - EVF = BW Syst. Contr. Lett. 55 2006 193 198
    • (2006) Syst. Contr. Lett. , vol.55 , pp. 193-198
    • Zhou, B.1    Duan, G.R.2
  • 44
    • 34249092654 scopus 로고    scopus 로고
    • Solutions to generalized Sylvester matrix equation by Schur decomposition
    • B. Zhou, and G.R. Duan Solutions to generalized Sylvester matrix equation by Schur decomposition Int. J. Syst. Sci. 38 2007 369 375
    • (2007) Int. J. Syst. Sci. , vol.38 , pp. 369-375
    • Zhou, B.1    Duan, G.R.2
  • 45
    • 58149346165 scopus 로고    scopus 로고
    • Weighted least squares solutions to general coupled Sylvester matrix equations
    • B. Zhou, Z.Y. Li, G.R. Duan, and Y. Wang Weighted least squares solutions to general coupled Sylvester matrix equations J. Comput. Appl. Math. 224 2009 759 776
    • (2009) J. Comput. Appl. Math. , vol.224 , pp. 759-776
    • Zhou, B.1    Li, Z.Y.2    Duan, G.R.3    Wang, Y.4
  • 46
    • 57049135287 scopus 로고    scopus 로고
    • Solutions to right coprime factorizations and generalized Sylvester matrix equations
    • B. Zhou, and Z.B. Yan Solutions to right coprime factorizations and generalized Sylvester matrix equations Trans. Inst. Measur. Contr. 30 2008 397 426
    • (2008) Trans. Inst. Measur. Contr. , vol.30 , pp. 397-426
    • Zhou, B.1    Yan, Z.B.2
  • 47
    • 43049136924 scopus 로고    scopus 로고
    • On the generalized Sylvester mapping and matrix equations
    • B. Zhou, and G.R. Duan On the generalized Sylvester mapping and matrix equations Syst. Contr. Lett. 57 2008 200 208
    • (2008) Syst. Contr. Lett. , vol.57 , pp. 200-208
    • Zhou, B.1    Duan, G.R.2
  • 48
    • 67349285076 scopus 로고    scopus 로고
    • On Smith-type iterative algorithms for the Stein matrix equation
    • B. Zhou, J. Lam, and G.R. Duan On Smith-type iterative algorithms for the Stein matrix equation Appl. Math. Lett. 22 2009 1038 1044
    • (2009) Appl. Math. Lett. , vol.22 , pp. 1038-1044
    • Zhou, B.1    Lam, J.2    Duan, G.R.3
  • 49
    • 61449108996 scopus 로고    scopus 로고
    • Gradient based iterative algorithm for solving coupled matrix equations
    • B. Zhou, G.R. Duan, and Z.Y. Li Gradient based iterative algorithm for solving coupled matrix equations Syst. Contr. Lett. 58 2009 327 333
    • (2009) Syst. Contr. Lett. , vol.58 , pp. 327-333
    • Zhou, B.1    Duan, G.R.2    Li, Z.Y.3
  • 50
    • 67349171081 scopus 로고    scopus 로고
    • Solutions to a family of matrix equations by using the Kronecker matrix polynomials
    • B. Zhou, Z.Y. Li, G.R. Duan, and Y. Wang Solutions to a family of matrix equations by using the Kronecker matrix polynomials Appl. Math. Comput. 212 2009 327 336
    • (2009) Appl. Math. Comput. , vol.212 , pp. 327-336
    • Zhou, B.1    Li, Z.Y.2    Duan, G.R.3    Wang, Y.4
  • 51
    • 77951139860 scopus 로고    scopus 로고
    • Iterative methods for solving linear matrix equation and linear matrix system
    • Y. Su, and G. Chen Iterative methods for solving linear matrix equation and linear matrix system Int. J. Comput. Math. 87 2010 763 774
    • (2010) Int. J. Comput. Math. , vol.87 , pp. 763-774
    • Su, Y.1    Chen, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.