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Volumn 23, Issue , 2012, Pages 1001-1022

Iterative method for the least squares problem of a matrix equation with tridiagonal matrix constraint

Author keywords

Least squares tridiagonal solution; Matrix iterative method; Matrix Krylov subspace; Preconditioner

Indexed keywords


EID: 84908258750     PISSN: 15379582     EISSN: 10813810     Source Type: Journal    
DOI: 10.13001/1081-3810.1571     Document Type: Article
Times cited : (1)

References (21)
  • 3
    • 38049084653 scopus 로고
    • Symmetric solution of linear matrix equations by matrix decomposition
    • K.E. Chu. Symmetric solution of linear matrix equations by matrix decomposition. Linear Algebra Appl., 119:35–50, 1989.
    • (1989) Linear Algebra Appl , vol.119 , pp. 35-50
    • Chu, K.E.1
  • 4
    • 1842865576 scopus 로고    scopus 로고
    • Least squares solution of BXAT = T over symmetric, skew-symmetric, and positive semidefinite X*
    • Y.B. Deng, X.Y. Hu, and L. Zhang. Least squares solution of BXAT = T over symmetric, skew-symmetric, and positive semidefinite X*. SIAM J. Matrix Anal. Appl., 25:486–494, 2003.
    • (2003) SIAM J. Matrix Anal. Appl , vol.25 , pp. 486-494
    • Deng, Y.B.1    Hu, X.Y.2    Zhang, L.3
  • 6
    • 27844473261 scopus 로고    scopus 로고
    • Matrix Krylov subspace methods for linear systems with multiple right-hand sides
    • M. Heyouni and A. Essai. Matrix Krylov subspace methods for linear systems with multiple right-hand sides. Numer. Algorithms, 40:137–156, 2005.
    • (2005) Numer. Algorithms , vol.40 , pp. 137-156
    • Heyouni, M.1    Essai, A.2
  • 7
    • 0001930482 scopus 로고
    • Matrix nearness problems and applications
    • M.J.C. Gover and S. Barnett (editors), Oxford University Press
    • N.J. Higham. Matrix nearness problems and applications. In M.J.C. Gover and S. Barnett (editors), Applications of Matrix Theory. Oxford University Press, 1–27, 1989.
    • (1989) Applications of Matrix Theory , pp. 1-27
    • Higham, N.J.1
  • 8
    • 33747873198 scopus 로고    scopus 로고
    • An iterative method for the least squares symmetric solution of matrix equation AXB = C
    • J.J. Hou, Z.Y. Peng, and X.L. Zhang. An iterative method for the least squares symmetric solution of matrix equation AXB = C. Numer. Algorithms, 42:181–192, 2006.
    • (2006) Numer. Algorithms , vol.42 , pp. 181-192
    • Hou, J.J.1    Peng, Z.Y.2    Zhang, X.L.3
  • 9
    • 0033197189 scopus 로고    scopus 로고
    • Global FOM and GMRES algorithms for matrix equations
    • K. Jbilou, A. Messaoudi, and H. Sadok. Global FOM and GMRES algorithms for matrix equations. Appl. Numer. Math., 31:49–63, 1999.
    • (1999) Appl. Numer. Math , vol.31 , pp. 49-63
    • Jbilou, K.1    Messaoudi, A.2    Sadok, H.3
  • 10
    • 0008402128 scopus 로고
    • Incomplete methods for solving ATAx = b
    • A. Jennings and M.A. Ajiz. Incomplete methods for solving ATAx = b. SIAM J. Sci. Comput., 5:978–987, 1984.
    • (1984) SIAM J. Sci. Comput , vol.5 , pp. 978-987
    • Jennings, A.1    Ajiz, M.A.2
  • 11
    • 18344377183 scopus 로고    scopus 로고
    • Updating of the viscous damping matrix from incomplete modal experimental data
    • (in Chinese)
    • C.F. Kong and H. Dai. Updating of the viscous damping matrix from incomplete modal experimental data. J. Vib. Eng., 18(1):85–90, 2005 (in Chinese).
    • (2005) J. Vib. Eng , vol.18 , Issue.1 , pp. 85-90
    • Kong, C.F.1    Dai, H.2
  • 12
    • 34247628970 scopus 로고    scopus 로고
    • A minimal residual algorithm for the inconsistent matrix equation AXB = C over symmetric matrices
    • Y. Lei and A.P. Liao. A minimal residual algorithm for the inconsistent matrix equation AXB = C over symmetric matrices. Appl. Math. Comput., 188:499–513, 2007.
    • (2007) Appl. Math. Comput , vol.188 , pp. 499-513
    • Lei, Y.1    Liao, A.P.2
  • 13
    • 33746129007 scopus 로고    scopus 로고
    • Least-squares solution of AXB = D over symmetric positive semidefinite matrices X
    • A.P. Liao and Z.Z. Bai. Least-squares solution of AXB = D over symmetric positive semidefinite matrices X. J. Comput. Math., 21:175–182, 2003.
    • (2003) J. Comput. Math , vol.21 , pp. 175-182
    • Liao, A.P.1    Bai, Z.Z.2
  • 14
    • 34648816411 scopus 로고    scopus 로고
    • Optimal approximate solution of the matrix equation AXB = C over symmetric matrices
    • A.P. Liao and Y. Lei. Optimal approximate solution of the matrix equation AXB = C over symmetric matrices. J. Comput. Math., 25:543–552, 2007.
    • (2007) J. Comput. Math , vol.25 , pp. 543-552
    • Liao, A.P.1    Lei, Y.2
  • 15
    • 0038957121 scopus 로고
    • L-structured matrices and linear matrix equations
    • J.R. Magnus. L-structured matrices and linear matrix equations. Linear Multilinear Algebra, 14:67–88, 1983.
    • (1983) Linear Multilinear Algebra , vol.14 , pp. 67-88
    • Magnus, J.R.1
  • 16
    • 0039943513 scopus 로고
    • LSQR: An algorithm for sparse linear equations and sparse least squares
    • C.C. Paige and A. Saunders. LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Software, 8(1):43–71, 1982.
    • (1982) ACM Trans. Math. Software , vol.8 , Issue.1 , pp. 43-71
    • Paige, C.C.1    Saunders, A.2
  • 17
    • 33846938283 scopus 로고    scopus 로고
    • Matrix iterative solutions to the least squares problem of BXAT = F with some linear constraints
    • Y.Y. Qiu, Z.Y. Zhang, and J.F. Lu. Matrix iterative solutions to the least squares problem of BXAT = F with some linear constraints. Appl. Math. Comput., 185:284–300, 2007.
    • (2007) Appl. Math. Comput , vol.185 , pp. 284-300
    • Qiu, Y.Y.1    Zhang, Z.Y.2    Lu, J.F.3
  • 18
    • 27344455755 scopus 로고    scopus 로고
    • Beijing University of Aeronautics and Astronautics Press, Beijing, (in Chinese)
    • R.C. Wang. Functional Analysis and Optimization Theory. Beijing University of Aeronautics and Astronautics Press, Beijing, 2003 (in Chinese).
    • (2003) Functional Analysis and Optimization Theory
    • Wang, R.C.1
  • 19
    • 0031082735 scopus 로고    scopus 로고
    • CIMGS: An incomplete orhtogonal factorization preconditionier
    • X. Wang, K.A. Gallivan, and R. Bramley. CIMGS: An incomplete orhtogonal factorization preconditionier. SIAM J. Sci. Comput., 18:516–536, 1997.
    • (1997) SIAM J. Sci. Comput , vol.18 , pp. 516-536
    • Wang, X.1    Gallivan, K.A.2    Bramley, R.3
  • 20
    • 27344436251 scopus 로고    scopus 로고
    • The optimal solution of linear matrix equation by using matrix decompositions
    • (in Chinese)
    • Y.X. Yuan. The optimal solution of linear matrix equation by using matrix decompositions. Math. Numer. Sin., 24:165–176, 2002 (in Chinese).
    • (2002) Math. Numer. Sin , vol.24 , pp. 165-176
    • Yuan, Y.X.1
  • 21
    • 0141636504 scopus 로고    scopus 로고
    • National Defence and Industry Press, Beijing, (in Chinese)
    • J.H. Zhang. Modeling of Dynamical Systems. National Defence and Industry Press, Beijing, 2000 (in Chinese).
    • (2000) Modeling of Dynamical Systems
    • Zhang, J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.