메뉴 건너뛰기




Volumn 48, Issue 4, 2012, Pages 621-635

A randomized method for solving discrete ill-posed problems

Author keywords

Discrete ill posed problem; Random projection; Regularization

Indexed keywords

EULER EQUATIONS; SYSTEMS ANALYSIS;

EID: 85027956005     PISSN: 10600396     EISSN: 15738337     Source Type: Journal    
DOI: 10.1007/s10559-012-9443-6     Document Type: Article
Times cited : (20)

References (32)
  • 1
    • 85050327257 scopus 로고    scopus 로고
    • P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion, SIAM, Philadelphia (1998).
    • P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion, SIAM, Philadelphia (1998).
  • 2
    • 84989319374 scopus 로고    scopus 로고
    • Optimization of inverse problem solution to obtain the distribution density function for surface contaminations
    • Yu. L. Zabulonov, Yu. M. Korostil, and E. G. Revunova, "Optimization of inverse problem solution to obtain the distribution density function for surface contaminations," Modeling and Information Technologies, 39, 77-83 (2006).
    • (2006) Modeling and Information Technologies , vol.39 , pp. 77-83
    • Zabulonov, Y.L.1    Korostil, Y.M.2    Revunova, E.G.3
  • 3
    • 85050321266 scopus 로고    scopus 로고
    • A. N. Tikhonov and V. Y. Arsenin, Methods for Solving Ill-Posed Problems [in Russian], Nauka, Moscow (1979).
    • A. N. Tikhonov and V. Y. Arsenin, Methods for Solving Ill-Posed Problems [in Russian], Nauka, Moscow (1979).
  • 4
    • 85050320883 scopus 로고    scopus 로고
    • V. A. Morozov, Regular Methods for Solving Ill-Posed Problems [in Russian], Nauka, Moscow (1987).
    • V. A. Morozov, Regular Methods for Solving Ill-Posed Problems [in Russian], Nauka, Moscow (1987).
  • 5
    • 85050325735 scopus 로고    scopus 로고
    • H. W. Engl, M. Hanke, and A. Neubaer, Regularization of Inverse Problems, Kluwer, Dordrecht (2000).
    • H. W. Engl, M. Hanke, and A. Neubaer, Regularization of Inverse Problems, Kluwer, Dordrecht (2000).
  • 6
    • 84858015097 scopus 로고    scopus 로고
    • Vector and distributed representations reflecting semantic relatedness of words
    • I. S. Misuno, D. A. Rachkovskij, and S. V. Slipchenko, "Vector and distributed representations reflecting semantic relatedness of words," Math. Machy i Systemy, No. 3, 50-67 (2005).
    • (2005) Math. Machy i Systemy , Issue.3 , pp. 50-67
    • Misuno, I.S.1    Rachkovskij, D.A.2    Slipchenko, S.V.3
  • 7
    • 85027935922 scopus 로고    scopus 로고
    • Randomized projective methods for the construction of binary sparse vector representations
    • D. A. Rachkovskij, I. S. Misuno, and S. V. Slipchenko, "Randomized projective methods for the construction of binary sparse vector representations," Cybernetics and Systems Analysis, Vol. 48, No. 1, 140-150 (2012).
    • (2012) Cybernetics and Systems Analysis , vol.48 , Issue.1 , pp. 140-150
    • Rachkovskij, D.A.1    Misuno, I.S.2    Slipchenko, S.V.3
  • 9
    • 85028117910 scopus 로고    scopus 로고
    • Study of error components for solving inverse problems using random projections
    • E. G. Revunova, "Study of error components for solving inverse problems using random projections," Mat. Mashiny i Sistemy, No. 4, 33-42 (2010).
    • Mat. Mashiny i Sistemy , vol.33-42 , Issue.4 , pp. 2010
    • Revunova, E.G.1
  • 10
    • 85050326606 scopus 로고    scopus 로고
    • P. Drineas, M. W. Mahoney, S. Muthukrishnan, and T. Sarlos, "Faster least squares approximation," Tech. Rep., arXiv: 0710.1435 (2007).
    • P. Drineas, M. W. Mahoney, S. Muthukrishnan, and T. Sarlos, "Faster least squares approximation," Tech. Rep., arXiv: 0710.1435 (2007).
  • 11
    • 0001632418 scopus 로고
    • The use of L-curve in the regularization of discrete ill-posed problems
    • P. C. Hansen and D. P. O'Leary, "The use of L-curve in the regularization of discrete ill-posed problems," SIAM J. Sci. Comput., 14, 1487-1503 (1993).
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 1487-1503
    • Hansen, P.C.1    O'Leary, D.P.2
  • 12
    • 32044449925 scopus 로고
    • Generalized cross-validation as a method for choosing a good ridge parameter
    • G. H. Golub, M. Heath, and G. Wahba, "Generalized cross-validation as a method for choosing a good ridge parameter," Technometrics, Vol. 21, No. 2, 215-223 (1979).
    • (1979) Technometrics , vol.21 , Issue.2 , pp. 215-223
    • Golub, G.H.1    Heath, M.2    Wahba, G.3
  • 13
    • 84919788213 scopus 로고    scopus 로고
    • Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions
    • N. Halko, P. G. Martinsson, and J. A. Tropp, "Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions," ACM Rep. Caltech, No. 5, 1-82 (2009).
    • (2009) ACM Rep. Caltech , Issue.5 , pp. 1-82
    • Halko, N.1    Martinsson, P.G.2    Tropp, J.A.3
  • 16
    • 0001654702 scopus 로고
    • Extensions of Lipschitz mappings into a Hilbert space
    • W. B. Johnson and J. Lindenstrauss, "Extensions of Lipschitz mappings into a Hilbert space," Contemporary Mathematics, No. 26, 189-206 (1984).
    • (1984) Contemporary Mathematics , Issue.26 , pp. 189-206
    • Johnson, W.B.1    Lindenstrauss, J.2
  • 18
    • 0038166193 scopus 로고    scopus 로고
    • Database-friendly random projections: Johnson-Lindenstrauss with binary coins
    • D. Achlioptas, "Database-friendly random projections: Johnson-Lindenstrauss with binary coins," J. Comput. System Sci., 66, No. 4, 671-687 (2003).
    • (2003) J. Comput. System Sci. , vol.66 , Issue.4 , pp. 671-687
    • Achlioptas, D.1
  • 20
    • 35348901208 scopus 로고    scopus 로고
    • Improved approximation algorithms for large matrices via random projections
    • T. Sarlos, "Improved approximation algorithms for large matrices via random projections," in: Proc. 47th Annual IEEE Symp. on Foundations of Computer Sci. (2006), pp. 143-152.
    • (2006) Proc. 47th Annual IEEE Symp. on Foundations of Computer Sci , pp. 143-152
    • Sarlos, T.1
  • 21
    • 51649090940 scopus 로고    scopus 로고
    • A fast randomized algorithm for overdetermined linear least-squares regression
    • V. Rokhlin and M. Tygert, "A fast randomized algorithm for overdetermined linear least-squares regression," PNAS, 105(36), 13212-13217 (2008).
    • (2008) PNAS , vol.105 , Issue.36 , pp. 13212-13217
    • Rokhlin, V.1    Tygert, M.2
  • 22
    • 85050323762 scopus 로고    scopus 로고
    • M. Tygert, "A fast algorithm for computing minimal-norm solutions to underdetermined systems of linear equations," Tech. Rep. N09-48, arXiv: 0905.4745, May 2009 (2009).
    • M. Tygert, "A fast algorithm for computing minimal-norm solutions to underdetermined systems of linear equations," Tech. Rep. N09-48, arXiv: 0905.4745, May 2009 (2009).
  • 23
    • 0000482137 scopus 로고    scopus 로고
    • On the relationship between generalization error, hypothesis complexity, and sample complexity for radial basis functions
    • P. Niyogi and F. Girosi, "On the relationship between generalization error, hypothesis complexity, and sample complexity for radial basis functions," Neural Comput., 8, 819-842 (1996).
    • (1996) Neural Comput. , vol.8 , pp. 819-842
    • Niyogi, P.1    Girosi, F.2
  • 24
    • 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, 1-35 (1994).
    • (1994) Numer. Algorithms , vol.6 , pp. 1-35
    • Hansen, P.C.1
  • 25
    • 0016355478 scopus 로고
    • A new look at the statistical model identification
    • H. Akaike, "A new look at the statistical model identification, " IEEE Trans. Automatic Control, Vol. 19, No. 6, 716-723 (1974).
    • (1974) IEEE Trans. Automatic Control , vol.19 , Issue.6 , pp. 716-723
    • Akaike, H.1
  • 26
    • 84915425007 scopus 로고
    • Some comments on C p
    • C. L. Mallows, "Some comments on C p, " Technometrics, 15, No. 4, 661-675 (1973).
    • (1973) Technometrics , vol.15 , Issue.4 , pp. 661-675
    • Mallows, C.L.1
  • 27
    • 0141879236 scopus 로고    scopus 로고
    • Model selection and minimum description length principle
    • M. Hansen and B. Yu, "Model selection and minimum description length principle," J. Amer. Statist. Assoc., 96, 746-774 (2001).
    • (2001) J. Amer. Statist. Assoc. , vol.96 , pp. 746-774
    • Hansen, M.1    Yu, B.2
  • 28
    • 0035434818 scopus 로고    scopus 로고
    • Subspace information criterion for model selection
    • M. Sugiyama and H. Ogawa, "Subspace information criterion for model selection," Neural Comput., Vol. 13, No. 8, 1863-1889 (2001).
    • (2001) Neural Comput. , vol.13 , Issue.8 , pp. 1863-1889
    • Sugiyama, M.1    Ogawa, H.2
  • 29
    • 85050328747 scopus 로고    scopus 로고
    • J. Rissanen, Lectures on Statistical Modeling Theory, Univ. of Technology, Tampere (2002), http://www.cs.tut.fi/~rissanen/.
    • J. Rissanen, Lectures on Statistical Modeling Theory, Univ. of Technology, Tampere (2002), http://www.cs.tut.fi/~rissanen/.
  • 32
    • 0036684726 scopus 로고    scopus 로고
    • Efficient determination of multiple regularization parameters in a generalized L-curve framework
    • M. Belge, M. E. Kilmer, and E. L. Miller, "Efficient determination of multiple regularization parameters in a generalized L-curve framework," Inverse Problems, 18, 1161-1183 (2002).
    • (2002) Inverse Problems , vol.18 , pp. 1161-1183
    • Belge, M.1    Kilmer, M.E.2    Miller, E.L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.