메뉴 건너뛰기




Volumn 25, Issue 3, 2008, Pages 335-366

A fast randomized algorithm for the approximation of matrices

Author keywords

Algorithm; Fast; Lanczos; Low rank; Matrix; QR; Randomized; SVD

Indexed keywords

APPROXIMATION ALGORITHMS; POLYNOMIAL APPROXIMATION;

EID: 53049094679     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2007.12.002     Document Type: Article
Times cited : (335)

References (21)
  • 1
    • 53049089509 scopus 로고    scopus 로고
    • N. Ailon, B. Chazelle, Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform, SIAM J. Comput. (2007), in press
    • N. Ailon, B. Chazelle, Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform, SIAM J. Comput. (2007), in press
  • 2
    • 53049102510 scopus 로고    scopus 로고
    • N. Ailon, E. Liberty, Fast dimension reduction using Rademacher series on dual BCH codes, Tech. rep. 1385, Yale University, Department of Computer Science, July 2007
    • N. Ailon, E. Liberty, Fast dimension reduction using Rademacher series on dual BCH codes, Tech. rep. 1385, Yale University, Department of Computer Science, July 2007
  • 3
    • 0027206124 scopus 로고    scopus 로고
    • S. Ar, M. Blum, B. Codenotti, P. Gemmell, Checking approximate computations over the reals, in: Proc. 25th Annual ACM Symposium on the Theory of Computing, 1993, pp. 786-795
    • S. Ar, M. Blum, B. Codenotti, P. Gemmell, Checking approximate computations over the reals, in: Proc. 25th Annual ACM Symposium on the Theory of Computing, 1993, pp. 786-795
  • 4
    • 0001326391 scopus 로고
    • Some applications of the rank-revealing QR factorization
    • Chan T.F., and Hansen P.C. Some applications of the rank-revealing QR factorization. SIAM J. Sci. Statist. Comput. 13 (1992) 727-741
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 727-741
    • Chan, T.F.1    Hansen, P.C.2
  • 6
    • 0001290746 scopus 로고
    • Estimating extremal eigenvalues and condition numbers of matrices
    • Dixon J.D. Estimating extremal eigenvalues and condition numbers of matrices. SIAM J. Numer. Anal. 20 (1983) 812-814
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 812-814
    • Dixon, J.D.1
  • 7
    • 53049101632 scopus 로고    scopus 로고
    • P. Drineas, M. Mahoney, S. Muthukrishnan, Polynomial time algorithm for column-row-based relative-error low-rank matrix approximation, Tech. rep. 2006-04, DIMACS, March 2006
    • P. Drineas, M. Mahoney, S. Muthukrishnan, Polynomial time algorithm for column-row-based relative-error low-rank matrix approximation, Tech. rep. 2006-04, DIMACS, March 2006
  • 9
    • 0037790752 scopus 로고    scopus 로고
    • The maximal-volume concept in approximation by low-rank matrices
    • Structured Matrices in Mathematics, Computer Science, and Engineering I, Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference, University of Colorado, Boulder, June 27-July 1, 1999. Olshevsky V. (Ed), AMS, Providence, RI
    • Goreinov S.A., and Tyrtyshnikov E.E. The maximal-volume concept in approximation by low-rank matrices. In: Olshevsky V. (Ed). Structured Matrices in Mathematics, Computer Science, and Engineering I, Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference, University of Colorado, Boulder, June 27-July 1, 1999. Contemporary Mathematics vol. 280 (2001), AMS, Providence, RI
    • (2001) Contemporary Mathematics , vol.280
    • Goreinov, S.A.1    Tyrtyshnikov, E.E.2
  • 10
    • 0003216822 scopus 로고    scopus 로고
    • Efficient algorithms for computing a strong rank-revealing QR factorization
    • Gu M., and Eisenstat S.C. Efficient algorithms for computing a strong rank-revealing QR factorization. SIAM J. Sci. Comput. 17 (1996) 848-869
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 848-869
    • Gu, M.1    Eisenstat, S.C.2
  • 11
    • 0043178250 scopus 로고
    • Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start
    • Kuczyński J., and Woźniakowski H. Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start. SIAM J. Matrix Anal. Appl. 13 (1992) 1094-1122
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 1094-1122
    • Kuczyński, J.1    Woźniakowski, H.2
  • 12
    • 0034347391 scopus 로고    scopus 로고
    • Row reduction of a matrix and A = C a B
    • Lee S.L., and Strang G. Row reduction of a matrix and A = C a B. Amer. Math. Monthly 107 (2000) 681-688
    • (2000) Amer. Math. Monthly , vol.107 , pp. 681-688
    • Lee, S.L.1    Strang, G.2
  • 13
    • 85009289532 scopus 로고    scopus 로고
    • On interpolation and integration in finite-dimensional spaces of bounded functions
    • Martinsson P.-G., Rokhlin V., and Tygert M. On interpolation and integration in finite-dimensional spaces of bounded functions. Comm. Appl. Math. Comput. Sci. 1 (2006) 133-142
    • (2006) Comm. Appl. Math. Comput. Sci. , vol.1 , pp. 133-142
    • Martinsson, P.-G.1    Rokhlin, V.2    Tygert, M.3
  • 14
    • 53049096426 scopus 로고    scopus 로고
    • P.-G. Martinsson, V. Rokhlin, M. Tygert, A randomized algorithm for the approximation of matrices, Tech. rep. 1361, Yale University, Department of Computer Science, June 2006
    • P.-G. Martinsson, V. Rokhlin, M. Tygert, A randomized algorithm for the approximation of matrices, Tech. rep. 1361, Yale University, Department of Computer Science, June 2006
  • 16
    • 35348901208 scopus 로고    scopus 로고
    • T. Sarlós, Improved approximation algorithms for large matrices via random projections, in: Proc. FOCS 2006, 47th Annual IEEE Symposium on Foundations of Computer Science, October 2006, pp. 143-152
    • T. Sarlós, Improved approximation algorithms for large matrices via random projections, in: Proc. FOCS 2006, 47th Annual IEEE Symposium on Foundations of Computer Science, October 2006, pp. 143-152
  • 17
    • 53049085718 scopus 로고    scopus 로고
    • T. Sarlós, Improved approximation algorithms for large matrices via random projections, revised, extended long form, Manuscript in preparation, 2006, currently available at: http://www.ilab.sztaki.hu/~stamas/publications/rp-long.pdf
    • T. Sarlós, Improved approximation algorithms for large matrices via random projections, revised, extended long form, Manuscript in preparation, 2006, currently available at: http://www.ilab.sztaki.hu/~stamas/publications/rp-long.pdf
  • 18
    • 0027554491 scopus 로고
    • Efficient computation of the DFT with only a subset of input or output points
    • Sorensen H.V., and Burrus C.S. Efficient computation of the DFT with only a subset of input or output points. IEEE Trans. Signal Process. 41 (1993) 1184-1200
    • (1993) IEEE Trans. Signal Process. , vol.41 , pp. 1184-1200
    • Sorensen, H.V.1    Burrus, C.S.2
  • 19
    • 0038805356 scopus 로고    scopus 로고
    • Incomplete cross approximation in the mosaic-skeleton method
    • Tyrtyshnikov E.E. Incomplete cross approximation in the mosaic-skeleton method. Computing 64 (2000) 367-380
    • (2000) Computing , vol.64 , pp. 367-380
    • Tyrtyshnikov, E.E.1
  • 20
    • 53049104459 scopus 로고    scopus 로고
    • F. Woolfe, E. Liberty, V. Rokhlin, M. Tygert, A fast randomized algorithm for the approximation of matrices, Tech. rep. 1386, Yale University, Department of Computer Science, July 2007
    • F. Woolfe, E. Liberty, V. Rokhlin, M. Tygert, A fast randomized algorithm for the approximation of matrices, Tech. rep. 1386, Yale University, Department of Computer Science, July 2007
  • 21
    • 53049097595 scopus 로고    scopus 로고
    • F. Woolfe, E. Liberty, V. Rokhlin, M. Tygert, A fast randomized algorithm for the approximation of matrices-Preliminary report, Tech. rep. 1380, Yale University, Department of Computer Science, April 2007
    • F. Woolfe, E. Liberty, V. Rokhlin, M. Tygert, A fast randomized algorithm for the approximation of matrices-Preliminary report, Tech. rep. 1380, Yale University, Department of Computer Science, April 2007


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.