메뉴 건너뛰기




Volumn 8, Issue , 2001, Pages 83-93

Additional results on index splittings for drazin inverse solutions of singular linear systems

Author keywords

Comparison theorem; Drazin inverse; Group inverse; Index; Index splitting; Monotone iteration; Moore Penrose inverse; Proper splitting

Indexed keywords


EID: 0041681630     PISSN: 10813810     EISSN: None     Source Type: Journal    
DOI: 10.13001/1081-3810.1062     Document Type: Article
Times cited : (32)

References (30)
  • 1
    • 0031485176 scopus 로고    scopus 로고
    • Existence and uniqueness of splittings for stationary iterative methods with applications to alternating methods
    • M. Benzi and D.B. Szyld. Existence and uniqueness of splittings for stationary iterative methods with applications to alternating methods. Numer. Math., 76:309-321, 1997.
    • (1997) Numer. Math. , vol.76 , pp. 309-321
    • Benzi, M.1    Szyld, D.B.2
  • 2
    • 0001218203 scopus 로고
    • Proper splittings of rectangular matrices
    • A. Berman and M. Neumann. Proper splittings of rectangular matrices. SIAM J. Appl. Math., 31:307-312, 1976.
    • (1976) SIAM J. Appl. Math. , vol.31 , pp. 307-312
    • Berman, A.1    Neumann, M.2
  • 3
    • 0016036113 scopus 로고
    • Cones and iterative methods for best least squares solutions of linear systems
    • A. Berman and R.J. Plemmons. Cones and iterative methods for best least squares solutions of linear systems. SIAM J. Numer. Anal., 11:145-154, 1974.
    • (1974) SIAM J. Numer. Anal. , vol.11 , pp. 145-154
    • Berman, A.1    Plemmons, R.J.2
  • 6
    • 3042578285 scopus 로고    scopus 로고
    • A new splitting for singular linear system and Drazin inverse
    • G. Chen and X. Chen. A new splitting for singular linear system and Drazin inverse. J. East China Norm. Univ. Natur. Sci. Ed., 3:12-18, 1996.
    • (1996) J. East China Norm. Univ. Natur. Sci. Ed. , vol.3 , pp. 12-18
    • Chen, G.1    Chen, X.2
  • 7
    • 0031361866 scopus 로고    scopus 로고
    • A semi-iterative method for real spectrum singular linear systems with an arbitrary index
    • J.J. Climent, M. Neumann, and A. Sidi. A semi-iterative method for real spectrum singular linear systems with an arbitrary index. J. Comput. Appl. Math., 87:21-38, 1997.
    • (1997) J. Comput. Appl. Math. , vol.87 , pp. 21-38
    • Climent, J.J.1    Neumann, M.2    Sidi, A.3
  • 9
    • 0001538079 scopus 로고
    • On the solution of singular systems of algebraic equations by semiiterative methods
    • M. Eiermann, I. Marek, and W. Niethammer. On the solution of singular systems of algebraic equations by semiiterative methods. Numer. Math., 53:265-283, 1988.
    • (1988) Numer. Math. , vol.53 , pp. 265-283
    • Eiermann, M.1    Marek, I.2    Niethammer, W.3
  • 10
    • 0001450532 scopus 로고
    • Comparisons of weak regular splittings and multisplitting methods
    • L. Elsner. Comparisons of weak regular splittings and multisplitting methods. Numer. Math., 56:283-289, 1989.
    • (1989) Numer. Math. , vol.56 , pp. 283-289
    • Elsner, L.1
  • 11
    • 84985316667 scopus 로고
    • On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling
    • R.W. Freund and M. Hochbruck. On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling. Numer. Linear Algebra Appl., 1:403-420, 1994.
    • (1994) Numer. Linear Algebra Appl. , vol.1 , pp. 403-420
    • Freund, R.W.1    Hochbruck, M.2
  • 12
    • 0000924593 scopus 로고
    • Numerical methods for solving linear least squares problems
    • G. Golub. Numerical methods for solving linear least squares problems. Numer. Math., 7:206-216, 1965.
    • (1965) Numer. Math. , vol.7 , pp. 206-216
    • Golub, G.1
  • 13
    • 0141965384 scopus 로고
    • Applications of the Drazin inverse to Cesaro-Neumann iterations
    • Pitman, London
    • R.E. Hartwig and F. Hall. Applications of the Drazin inverse to Cesaro-Neumann iterations. Recent Applications of Generalized Inverses, 66:145-195, Pitman, London, 1982.
    • (1982) Recent Applications of Generalized Inverses , vol.66 , pp. 145-195
    • Hartwig, R.E.1    Hall, F.2
  • 14
    • 0040901004 scopus 로고
    • Applications of Drazin inverse to the Hill cryptographic systems, Part III
    • R.E. Hartwig and J. Levine. Applications of Drazin inverse to the Hill cryptographic systems, Part III. Cryptologia 5;67-77, 1981.
    • (1981) Cryptologia , vol.5 , pp. 67-77
    • Hartwig, R.E.1    Levine, J.2
  • 15
    • 0035582264 scopus 로고    scopus 로고
    • Some additive results on Drazin inverse
    • R.E. Hartwig, G. Wang, and Y.M. Wei. Some additive results on Drazin inverse. Linear Algebra Appl., 322:207-217, 2001.
    • (2001) Linear Algebra Appl. , vol.322 , pp. 207-217
    • Hartwig, R.E.1    Wang, G.2    Wei, Y.M.3
  • 16
    • 0014817656 scopus 로고
    • A note on the solution of rectangular linear systems by iterations
    • V.N. Joshi. A note on the solution of rectangular linear systems by iterations. SIAM Rev., 12:463-466, 1970.
    • (1970) SIAM Rev. , vol.12 , pp. 463-466
    • Joshi, V.N.1
  • 17
    • 0001457518 scopus 로고
    • On the solution of singular systems and semidefinite linear systems by iterations
    • H.B. Keller. On the solution of singular systems and semidefinite linear systems by iterations. SIAM J. Numer. Anal., 2:281-290, 1965.
    • (1965) SIAM J. Numer. Anal. , vol.2 , pp. 281-290
    • Keller, H.B.1
  • 18
    • 0001759094 scopus 로고
    • Convergence of nested classical iterative methods for linear systems
    • P.J. Lanzkron, D.J. Rose, and D.B. Szyld. Convergence of nested classical iterative methods for linear systems. Numer. Math., 58:685-702, 1991.
    • (1991) Numer. Math. , vol.58 , pp. 685-702
    • Lanzkron, P.J.1    Rose, D.J.2    Szyld, D.B.3
  • 19
    • 0001731763 scopus 로고
    • Comparison theorems for weak splittings of bounded operators
    • I. Marek and D.B. Szyld. Comparison theorems for weak splittings of bounded operators. Numer. Math., 58:387-397, 1990.
    • (1990) Numer. Math. , vol.58 , pp. 387-397
    • Marek, I.1    Szyld, D.B.2
  • 20
    • 0012418796 scopus 로고
    • Successive overrelaxation methods for solving the rank deficient linear least squares problem
    • V.A. Miller and M. Neumann. Successive overrelaxation methods for solving the rank deficient linear least squares problem. Linear Algebra, Appl., 88/89:533-557, 1987.
    • (1987) Linear Algebra, Appl. , vol.88-89 , pp. 533-557
    • Miller, V.A.1    Neumann, M.2
  • 21
    • 0001469443 scopus 로고
    • Monotone iterations for nonlinear equations with applications to Gauss-Seidel methods
    • J.M. Ortega and W.C. Rheinboldt. Monotone iterations for nonlinear equations with applications to Gauss-Seidel methods. SIAM J. Numer. Anal., 4:171-190, 1967.
    • (1967) SIAM J. Numer. Anal. , vol.4 , pp. 171-190
    • Ortega, J.M.1    Rheinboldt, W.C.2
  • 22
    • 0010716924 scopus 로고
    • Nonnegative Drazin inverse
    • W.C. Pye. Nonnegative Drazin inverse. Linear Algebra Appl., 30:149-153, 1980.
    • (1980) Linear Algebra Appl. , vol.30 , pp. 149-153
    • Pye, W.C.1
  • 23
    • 0033457033 scopus 로고    scopus 로고
    • A unified approach to Krylov subspace methods for the Drazin-inverse solution of singular nonsymmetric linear systems
    • A. Sidi. A unified approach to Krylov subspace methods for the Drazin-inverse solution of singular nonsymmetric linear systems. Linear Algebra Appl., 298:99-113, 1999.
    • (1999) Linear Algebra Appl. , vol.298 , pp. 99-113
    • Sidi, A.1
  • 24
    • 3042624625 scopus 로고    scopus 로고
    • A representation of the minimal P-norm solution
    • To appear in
    • P.S. Stanimirovic. A representation of the minimal P-norm solution. To appear in Novi Sad J. Math.
    • Novi Sad J. Math.
    • Stanimirovic, P.S.1
  • 26
    • 0000409612 scopus 로고    scopus 로고
    • Index splitting for the Drazin inverse and the singular linear systems
    • Y.M. Wei. Index splitting for the Drazin inverse and the singular linear systems, Applied Math. Comput., 95:115-124, 1998.
    • (1998) Applied Math. Comput. , vol.95 , pp. 115-124
    • Wei, Y.M.1
  • 28
    • 0033890994 scopus 로고    scopus 로고
    • Convergence properties of Krylov subspace methods for singular linear systems with arbitrary index
    • Y.M. Wei and H.B. Wu. Convergence properties of Krylov subspace methods for singular linear systems with arbitrary index. J. Comput. Appl. Math., 114:305-318, 2000.
    • (2000) J. Comput. Appl. Math. , vol.114 , pp. 305-318
    • Wei, Y.M.1    Wu, H.B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.