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Volumn 149, Issue 2, 2004, Pages 411-422

Weighted Tikhonov filter matrices for ill-posed problems

Author keywords

Filter matrices; Rank deficient; Weighted pseudoinverse; Weighted Tikhonov regularization

Indexed keywords

ERROR ANALYSIS; LEAST SQUARES APPROXIMATIONS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

EID: 0348170680     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(03)00149-8     Document Type: Article
Times cited : (6)

References (13)
  • 2
    • 38249019376 scopus 로고
    • Equivalence of regularization and truncated iteration in the solution of ill-posed image reconstruction problems
    • Fleming H.E. Equivalence of regularization and truncated iteration in the solution of ill-posed image reconstruction problems. Linear Algebra Appl. 130:1990;133-150.
    • (1990) Linear Algebra Appl. , vol.130 , pp. 133-150
    • Fleming, H.E.1
  • 3
    • 0029341230 scopus 로고
    • Nonlinear image recovery with half-quadratic regularization
    • German D., Yang C. Nonlinear image recovery with half-quadratic regularization. IEEE Trans. Image Process. 4:1995;932-945.
    • (1995) IEEE Trans. Image Process. , vol.4 , pp. 932-945
    • German, D.1    Yang, C.2
  • 4
    • 0034353667 scopus 로고    scopus 로고
    • The use and properties of Tikhonov filter matrices
    • Gulliksson M., Wedin P.Å. The use and properties of Tikhonov filter matrices. SIAM J. Matrix Anal. Appl. 22:2000;276-281.
    • (2000) SIAM J. Matrix Anal. Appl. , vol.22 , pp. 276-281
    • Gulliksson, M.1    Wedin, P.Å.2
  • 5
    • 0011120580 scopus 로고    scopus 로고
    • Perturbation identities for regularized Tikhonov inverses and weighted pseudoinverses
    • Gulliksson M., Wedin P.Å., Wei Y. Perturbation identities for regularized Tikhonov inverses and weighted pseudoinverses. BIT. 40:2000;513-523.
    • (2000) BIT , vol.40 , pp. 513-523
    • Gulliksson, M.1    Wedin, P.Å.2    Wei, Y.3
  • 6
    • 31244432352 scopus 로고    scopus 로고
    • Perturbation bound for constrained and weighted least squares problem
    • Gulliksson M., Jin X., Wei Y. Perturbation bound for constrained and weighted least squares problem. Linear Algebra Appl. 349:2002;221-232.
    • (2002) Linear Algebra Appl. , vol.349 , pp. 221-232
    • Gulliksson, M.1    Jin, X.2    Wei, Y.3
  • 7
    • 0000803444 scopus 로고
    • The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate
    • Golub G., Pereyra V. The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. SIAM J. Numer. Anal. 10:1973;413-432.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 413-432
    • Golub, G.1    Pereyra, V.2
  • 8
    • 0003640980 scopus 로고    scopus 로고
    • Rank-Deficient and Discrete Ill-Posed Problems
    • Philadelphia, PA: SIAM
    • Hansen P.C. Rank-Deficient and Discrete Ill-Posed Problems. Numerical Aspects of LSIAM. 1998;SIAM, Philadelphia, PA.
    • (1998) Numerical Aspects of LSIAM
    • Hansen, P.C.1
  • 9
    • 0000195992 scopus 로고
    • Perturbation theory for pseudo-inverses
    • Wedin P.Å. Perturbation theory for pseudo-inverses. BIT. 13:1973;217-232.
    • (1973) BIT , vol.13 , pp. 217-232
    • Wedin, P.Å.1
  • 10
    • 0016926423 scopus 로고
    • Generalizing the singular value decomposition
    • Van Loan C.F. Generalizing the singular value decomposition. SIAM J. Numer. Anal. 13:1976;76-83.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 76-83
    • Van Loan, C.F.1
  • 11
    • 0038330476 scopus 로고
    • Perturbation theory for weighted Moore-Penrose inverse
    • in Chinese
    • Wang G. Perturbation theory for weighted Moore-Penrose inverse. Comm. Appl. Math. Comput. Math. 1:1987;48-60. in Chinese.
    • (1987) Comm. Appl. Math. Comput. Math. , vol.1 , pp. 48-60
    • Wang, G.1
  • 12
    • 0034159269 scopus 로고    scopus 로고
    • Expressions for the perturbation of the weighted Moore-Penrose inverse
    • Wei Y., Wu H. Expressions for the perturbation of the weighted Moore-Penrose inverse. Comput. Math. Appl. 39:2000;13-18.
    • (2000) Comput. Math. Appl. , vol.39 , pp. 13-18
    • Wei, Y.1    Wu, H.2
  • 13
    • 0035947468 scopus 로고    scopus 로고
    • The representation and approximation for the weighted Moore-Penrose inverse
    • Wei Y., Wu H. The representation and approximation for the weighted Moore-Penrose inverse. Appl. Math. Comput. 121:2001;17-28.
    • (2001) Appl. Math. Comput. , vol.121 , pp. 17-28
    • Wei, Y.1    Wu, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.