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Volumn 16, Issue 3, 2009, Pages 237-257

Preconditioners for ill-posed Toeplitz matrices with differentiable generating functions

Author keywords

Generating function; ill determined rank; Iterative regularization; Preconditioning; Toeplitz matrices

Indexed keywords


EID: 65749095908     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.635     Document Type: Article
Times cited : (2)

References (25)
  • 2
    • 0030246195 scopus 로고    scopus 로고
    • Conjugate gradient methods for Toeplitz systems
    • Chan RH, Ng MK. Conjugate gradient methods for Toeplitz systems. SIAM Review 1996; 38:427-482.
    • (1996) SIAM Review , vol.38 , pp. 427-482
    • Chan, R.H.1    Ng, M.K.2
  • 3
    • 0004117648 scopus 로고    scopus 로고
    • Toeplitz and Circulant Matrices: A Review
    • Available from:, [2000]
    • Gray R. Toeplitz and Circulant Matrices: A Review, 2000. Available from: http:www-isl.stanford.edu/~gray/toeplitz.pdf [2000].
    • (2000)
    • Gray, R.1
  • 5
    • 0042914754 scopus 로고    scopus 로고
    • Block {ω}-circulant preconditioners for the systems of differential equations
    • Bertaccini D, Ng MK. Block {ω}-circulant preconditioners for the systems of differential equations. Calcolo 2003; 40:71-90.
    • (2003) Calcolo , vol.40 , pp. 71-90
    • Bertaccini, D.1    Ng, M.K.2
  • 6
    • 20744455997 scopus 로고    scopus 로고
    • Analysis of a circulant based preconditioner for a class of lower rank extracted systems
    • Salapaka S, Peirce A, Dahleh M. Analysis of a circulant based preconditioner for a class of lower rank extracted systems. Numerical Linear Algebra with Applications 2005; 12:9-23.
    • (2005) Numerical Linear Algebra with Applications , vol.12 , pp. 9-23
    • Salapaka, S.1    Peirce, A.2    Dahleh, M.3
  • 8
    • 0000333315 scopus 로고
    • Preconditioned iterative regularization for ill-posed problems
    • In, Reichel L, Ruttan A, Varga RS (eds). De Gruyter: Berlin
    • Hanke M, Nagy JG, Plemmons RJ. Preconditioned iterative regularization for ill-posed problems. In Numerical Linear Algebra, Reichel L, Ruttan A, Varga RS (eds). De Gruyter: Berlin, 1993; 141-163.
    • (1993) Numerical Linear Algebra , pp. 141-163
    • Hanke, M.1    Nagy, J.G.2    Plemmons, R.J.3
  • 9
    • 0000696639 scopus 로고
    • On the rate of convergence of the preconditioned conjugate gradient method
    • Axelsson O, Lindskog G. On the rate of convergence of the preconditioned conjugate gradient method. Numerische Mathematik 1986; 48:499-523.
    • (1986) Numerische Mathematik , vol.48 , pp. 499-523
    • Axelsson, O.1    Lindskog, G.2
  • 11
    • 0033296755 scopus 로고    scopus 로고
    • A fast algorithm for deblurring models with Neumann boundary conditions
    • Ng MK, Chan RH, Tang WC. A fast algorithm for deblurring models with Neumann boundary conditions. SIAM Journal on Scientific Computing 1999; 21:851-866.
    • (1999) SIAM Journal on Scientific Computing , vol.21 , pp. 851-866
    • Ng, M.K.1    Chan, R.H.2    Tang, W.C.3
  • 12
    • 4043054296 scopus 로고    scopus 로고
    • A note on anti-reflective boundary conditions and fast deblurring models
    • Serra Capizzano S. A note on anti-reflective boundary conditions and fast deblurring models. SIAM Journal on Scientific Computing 2003; 25:1307-1325.
    • (2003) SIAM Journal on Scientific Computing , vol.25 , pp. 1307-1325
    • Capizzano, S.S.1
  • 13
    • 33846063791 scopus 로고    scopus 로고
    • Improved image deblurring with anti-reflective boundary conditions and re-blurring
    • Donatelli M, Estatico C, Martinelli A, Serra Capizzano S. Improved image deblurring with anti-reflective boundary conditions and re-blurring. Inverse Problems 2006; 22:2035-2054.
    • (2006) Inverse Problems , vol.22 , pp. 2035-2054
    • Donatelli, M.1    Estatico, C.2    Martinelli, A.3    Capizzano, S.S.4
  • 17
    • 0022694911 scopus 로고
    • A proposal for Toeplitz matrix calculations
    • Strang G. A proposal for Toeplitz matrix calculations. Studies in Applied Mathematics 1986; 74:171-176.
    • (1986) Studies in Applied Mathematics , vol.74 , pp. 171-176
    • Strang, G.1
  • 19
    • 0043236541 scopus 로고    scopus 로고
    • A class of filtering superoptimal preconditioners for highly ill-conditioned linear systems
    • Estatico C. A class of filtering superoptimal preconditioners for highly ill-conditioned linear systems. BIT 2002; 42:753-778.
    • (2002) BIT , vol.42 , pp. 753-778
    • Estatico, C.1
  • 20
    • 12444264871 scopus 로고    scopus 로고
    • A classification scheme for regularizing preconditioners, with application to Toeplitz systems
    • Estatico C. A classification scheme for regularizing preconditioners, with application to Toeplitz systems. Linear Algebra and its Applications 2005; 397:107-131.
    • (2005) Linear Algebra and its Applications , vol.397 , pp. 107-131
    • Estatico, C.1
  • 22
    • 0026908109 scopus 로고
    • Circulant preconditioners constructed from kernels
    • Chan RH, Yeung M. Circulant preconditioners constructed from kernels. SIAM Journal on Numerical Analysis 1992; 29:1093-1103.
    • (1992) SIAM Journal on Numerical Analysis , vol.29 , pp. 1093-1103
    • Chan, R.H.1    Yeung, M.2
  • 24
    • 0000463893 scopus 로고
    • An algorithm for the regularization of ill conditioned, banded least squares problems
    • Eldén L. An algorithm for the regularization of ill conditioned, banded least squares problems. SIAM Journal on Statistical and Scientific Computing 1984; 5:237-254.
    • (1984) SIAM Journal on Statistical and Scientific Computing , vol.5 , pp. 237-254
    • Eldén, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.