메뉴 건너뛰기




Volumn 21, Issue 6, 2000, Pages 2257-2274

Low-rank matrix approximation using the Lanczos bidiagonalization process with applications

Author keywords

[No Author keywords available]

Indexed keywords

LANCZOS ALGORITHMS; LANCZOS BIDIAGONALIZATION PROCESS; LOW RANK APPROXIMATION; SINGULAR VALUE DECOMPOSITION; SPACE MATRICES;

EID: 0034510473     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827597327309     Document Type: Article
Times cited : (127)

References (24)
  • 3
    • 0001925371 scopus 로고
    • A Lanczos algorithm for computing singular values and vectors of large matrices
    • J. CULLUM, R. A. WILLOUGHBY, AND M. LAKE, A Lanczos algorithm for computing singular values and vectors of large matrices, SIAM J. Sci. Statist. Comput., 4 (1983), pp. 197-215.
    • (1983) SIAM J. Sci. Statist. Comput. , vol.4 , pp. 197-215
    • Cullum, J.1    Willoughby, R.A.2    Lake, M.3
  • 5
    • 0000288016 scopus 로고
    • Calculating the singular values and pseudo-inverse of a matrix
    • G. GOLUB AND W. KAHAN, Calculating the singular values and pseudo-inverse of a matrix, SIAM J. Numer. Anal., 2 (1965), pp. 205-224.
    • (1965) SIAM J. Numer. Anal. , vol.2 , pp. 205-224
    • Golub, G.1    Kahan, W.2
  • 6
    • 0019576431 scopus 로고
    • A block Lanczos method for computing the singular values and corresponding singular vectors of a matrix
    • G. H. GOLUB, F. LUK, AND M. OVERTON, A block Lanczos method for computing the singular values and corresponding singular vectors of a matrix, ACM Trans. Math. Software, 7 (1981), pp. 149-169.
    • (1981) ACM Trans. Math. Software , vol.7 , pp. 149-169
    • Golub, G.H.1    Luk, F.2    Overton, M.3
  • 9
    • 0000374864 scopus 로고
    • Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank
    • P. C. HANSEN, Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank, SIAM J. Sci. Statist. Comput., 11 (1990), pp. 503-518.
    • (1990) SIAM J. Sci. Statist. Comput. , vol.11 , pp. 503-518
    • Hansen, P.C.1
  • 11
    • 20344394051 scopus 로고    scopus 로고
    • Matrix Market, http://math.nist.gov/MatrixMarket/.
    • Matrix Market
  • 12
    • 84962560070 scopus 로고    scopus 로고
    • MultiSpec, http://dynamo.ecn.purdue.edu/~biehl/MultiSpec/documentation.html.
    • MultiSpec
  • 13
    • 0027561417 scopus 로고
    • Low-dimensional representation of faces in higher dimensions of the face space
    • A. O'TOOLE, H. ABDI, K. A. DEFPENBACHER, AND D. VALENTIN, Low-dimensional representation of faces in higher dimensions of the face space, J. Amer. Optical Soc., 10 (1993), pp. 405-411.
    • (1993) J. Amer. Optical Soc. , vol.10 , pp. 405-411
    • O'Toole, A.1    Abdi, H.2    Defpenbacher, K.A.3    Valentin, D.4
  • 14
    • 53849148874 scopus 로고
    • Error analysis of the Lanczos algorithm for tridiagonalizing a symmetric matrix
    • C. C. PAIGE, Error analysis of the Lanczos algorithm for tridiagonalizing a symmetric matrix, J. Inst. Math. Appl., 18 (1976), pp. 341-349.
    • (1976) J. Inst. Math. Appl. , vol.18 , pp. 341-349
    • Paige, C.C.1
  • 15
    • 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
  • 17
    • 0030167884 scopus 로고    scopus 로고
    • Photobook: Content-based manipulation of image databases
    • A. PETLAND, R. W. PICARD, AND S. SCLAROFF, Photobook: Content-based manipulation of image databases, Internat. J. Comput. Vision, 18 (1996), pp. 233-254.
    • (1996) Internat. J. Comput. Vision , vol.18 , pp. 233-254
    • Petland, A.1    Picard, R.W.2    Sclaroff, S.3
  • 19
    • 0000682936 scopus 로고
    • Analysis for the symmetric Lanczos algorithm with reorthogonalization
    • H. D. SIMON, Analysis for the symmetric Lanczos algorithm with reorthogonalization, Linear Algebra Appl., 61 (1984), pp. 101-131.
    • (1984) Linear Algebra Appl. , vol.61 , pp. 101-131
    • Simon, H.D.1
  • 20
    • 84968519566 scopus 로고
    • The Lanczos algorithm with partial reorthogonalization
    • H. D. SIMON, The Lanczos algorithm with partial reorthogonalization, Math. Comp., 42 (1984), pp. 115-142.
    • (1984) Math. Comp. , vol.42 , pp. 115-142
    • Simon, H.D.1
  • 22
    • 0343980624 scopus 로고    scopus 로고
    • SVDPACK
    • SVDPACK, http://www.netlib.org/svdpack/index.html.
  • 23
    • 0343108684 scopus 로고    scopus 로고
    • Technical report 41, Max-Planck-Institute für biologische Kybernetik, Tübingen, Germany
    • N. E. TROJE AND T. VETTER, Representation of human faces, Technical report 41, Max-Planck-Institute für biologische Kybernetik, Tübingen, Germany, 1996.
    • (1996) Representation of Human Faces
    • Troje, N.E.1    Vetter, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.