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Volumn 14, Issue , 2002, Pages 20-35

L-curve curvature bounds via lanczos bidiagonalization

Author keywords

Gauss quadrature; Ill posed problem; L curve; Regularization

Indexed keywords


EID: 0037580308     PISSN: 10689613     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (55)

References (15)
  • 1
    • 0001644662 scopus 로고
    • A bidiagonalization algorithm for solving large and sparse ill-posed systems of linear equations
    • Å. Björck, A bidiagonalization algorithm for solving large and sparse ill-posed systems of linear equations, BIT 18 (1988), pp. 659-670.
    • (1988) BIT , vol.18 , pp. 659-670
    • Björck, Å.1
  • 2
    • 0000924088 scopus 로고    scopus 로고
    • Estimation of the L-curve via Lanczos bidiagonalization
    • D. Calvetti, G. H. Golub and L. Reichel, Estimation of the L-curve via Lanczos bidiagonalization, BIT 39 (1999), pp. 603-619.
    • (1999) BIT , vol.39 , pp. 603-619
    • Calvetti, D.1    Golub, G.H.2    Reichel, L.3
  • 3
    • 0034323326 scopus 로고    scopus 로고
    • Tikhonov regularization and the L-curve for large, discrete ill-posed problems
    • D. Calvetti, S. Morigi, L. Reichel and F. Sgallari, Tikhonov regularization and the L-curve for large, discrete ill-posed problems, J. Comput. Appl. Math. 123 (2000), pp. 423-446.
    • (2000) J. Comput. Appl. Math. , vol.123 , pp. 423-446
    • Calvetti, D.1    Morigi, S.2    Reichel, L.3    Sgallari, F.4
  • 4
    • 0034558885 scopus 로고    scopus 로고
    • An L-ribbon for large underdetermined linear discrete ill-posed problems
    • D. Calvetti, S. Morigi, L. Reichel and F. Sgallari, An L-ribbon for large underdetermined linear discrete ill-posed problems, Numer. Algorithms 25 (2000), pp. 89-107.
    • (2000) Numer. Algorithms , vol.25 , pp. 89-107
    • Calvetti, D.1    Morigi, S.2    Reichel, L.3    Sgallari, F.4
  • 5
    • 0000565315 scopus 로고
    • Algorithms for the regularization of ill-conditioned least squares problems
    • L. Eldén, Algorithms for the regularization of ill-conditioned least squares problems, BIT 17 (1977), pp. 134-145.
    • (1977) BIT , vol.17 , pp. 134-145
    • Eldén, L.1
  • 6
    • 0001070999 scopus 로고
    • Some modified matrix eigenvalue problems
    • G. H. Golub, Some modified matrix eigenvalue problems, SIAM Review 15 (1973), pp. 318-334.
    • (1973) SIAM Review , vol.15 , pp. 318-334
    • Golub, G.H.1
  • 7
    • 0003093333 scopus 로고
    • Matrices, moments and quadrature
    • eds. D. F. Griffiths and G. A. Watson, Longman, Essex, England
    • G. H. Golub and G. Meurant, Matrices, moments and quadrature, in Numerical Analysis 1993, eds. D. F. Griffiths and G. A. Watson, Longman, Essex, England, 1994, pp. 105-156.
    • (1993) Numerical Analysis , pp. 105-156
    • Golub, G.H.1    Meurant, G.2
  • 8
    • 0001678475 scopus 로고
    • Quadratically constrained least squares and quadratic problems
    • G. H. Golub and U. von Matt, Quadratically constrained least squares and quadratic problems, Numer. Math. 59 (1991), pp. 561-580.
    • (1991) Numer. Math. , vol.59 , pp. 561-580
    • Golub, G.H.1    Von Matt, U.2
  • 9
    • 0040354352 scopus 로고    scopus 로고
    • Tikhonov regularization for large scale problems
    • eds. G. H. Golub, S. H. Lui, F. Luk and R. Plemmons, Springer, New York
    • G. H. Golub and U. von Matt, Tikhonov regularization for large scale problems, in Workshop on Scientific Computing, eds. G. H. Golub, S. H. Lui, F. Luk and R. Plemmons, Springer, New York, 1997.
    • (1997) Workshop on Scientific Computing
    • Golub, G.H.1    Von Matt, U.2
  • 10
    • 0000570697 scopus 로고
    • Analysis of discrete ill-posed problems by means of the L-curve
    • P. C. Hansen, Analysis of discrete ill-posed problems by means of the L-curve, SIAM Review 34 (1992), pp. 561-580.
    • (1992) SIAM Review , vol.34 , pp. 561-580
    • Hansen, P.C.1
  • 11
    • 13344267706 scopus 로고
    • Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
    • P. C. Hansen, Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems, Numer. Algorithms 6 (1994), pp. 1-35. Software is available in Netlib at the web site http://www.netlib.org.
    • (1994) Numer. Algorithms , vol.6 , pp. 1-35
    • Hansen, P.C.1
  • 12
    • 0000236333 scopus 로고    scopus 로고
    • The L-curve and its use in the numerical treatment of inverse problems
    • Computational Inverse Problems in Electrocardiology, ed. P. Johnston, WIT Press, Southampton
    • P. C. Hansen, The L-curve and its use in the numerical treatment of inverse problems, in Computational Inverse Problems in Electrocardiology, ed. P. Johnston, Advances in Computational Bioengineering, vol. 4, WIT Press, Southampton, 2000, pp. 119-142.
    • (2000) Advances in Computational Bioengineering , vol.4 , pp. 119-142
    • Hansen, P.C.1
  • 13
    • 0001632418 scopus 로고
    • The use of the L-curve in the regularization of discrete ill-posed problems
    • P. C. Hansen and D. P. O'Leary, The use of the L-curve in the regularization of discrete ill-posed problems, SIAM J. Sci. Comput. 14 (1993), pp. 1487-1503.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 1487-1503
    • Hansen, P.C.1    O'Leary, D.P.2
  • 14
    • 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. Software 8 (1982), pp. 43-71.
    • (1982) ACM Trans. Math. Software , vol.8 , pp. 43-71
    • Paige, C.C.1    Saunders, M.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.