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Volumn 36, Issue 1, 2006, Pages 132-157

Fast Monte Carlo algorithms for matrices I: Approximating matrix multiplication

Author keywords

Massive data sets; Matrix multiplication; Monte Carlo methods; Randomized algorithms; Streaming models

Indexed keywords

MASSIVE DATA SETS; MATRIX MULTIPLICATION; RANDOMIZED ALGORITHMS; STREAMING MODELS;

EID: 33751115359     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539704442684     Document Type: Article
Times cited : (419)

References (28)
  • 1
    • 34247228045 scopus 로고    scopus 로고
    • Fast computation of low rank matrix approximations
    • to appear
    • D. ACHLIOPTAS AND F. MCSHERRY, Fast computation of low rank matrix approximations, J. ACM, to appear.
    • J. ACM
    • ACHLIOPTAS, D.1    MCSHERRY, F.2
  • 6
    • 0004151496 scopus 로고    scopus 로고
    • Springer-Verlag, New York
    • R. BHATIA, Matrix Analysis, Springer-Verlag, New York, 1997.
    • (1997) Matrix Analysis
    • BHATIA, R.1
  • 7
    • 0006670574 scopus 로고    scopus 로고
    • Approximating matrix multiplication for pattern recognition tasks
    • E. COHEN AND D. D. LEWIS, Approximating matrix multiplication for pattern recognition tasks, J. Algorithms, 30 (1999), pp. 211-252.
    • (1999) J. Algorithms , vol.30 , pp. 211-252
    • COHEN, E.1    LEWIS, D.D.2
  • 8
    • 85023205150 scopus 로고
    • Matrix multiplication via arithmetic progressions
    • D. COPPERSMITH AND S. WINOGRAD, Matrix multiplication via arithmetic progressions, J. Symbolic Comput., 9 (1990), pp. 251-280.
    • (1990) J. Symbolic Comput , vol.9 , pp. 251-280
    • COPPERSMITH, D.1    WINOGRAD, S.2
  • 11
    • 33751075906 scopus 로고    scopus 로고
    • Fast Monte Carlo algorithms for matrices II: Computing a low-rank approximation to a matrix
    • P. DRINEAS, R. KANNAN, AND M. W. MAHONEY, Fast Monte Carlo algorithms for matrices II: Computing a low-rank approximation to a matrix, SIAM J. Comput., 36 (2006), pp. 158-183.
    • (2006) SIAM J. Comput , vol.36 , pp. 158-183
    • DRINEAS, P.1    KANNAN, R.2    MAHONEY, M.W.3
  • 12
    • 33751097630 scopus 로고    scopus 로고
    • Fast Monte Carlo algorithms for matrices III: Computing a compressed approximate matrix decomposition
    • P. DRINEAS, R. KANNAN, AND M. W. MAHONEY, Fast Monte Carlo algorithms for matrices III: Computing a compressed approximate matrix decomposition, SIAM J. Comput., 36 (2006), pp. 184-206.
    • (2006) SIAM J. Comput , vol.36 , pp. 184-206
    • DRINEAS, P.1    KANNAN, R.2    MAHONEY, M.W.3
  • 16
    • 51249182622 scopus 로고
    • The eigenvalues of random symmetric matrices
    • Z. FÜREDI AND J. KOMLOS, The eigenvalues of random symmetric matrices, Combinatorica, 1 (1981), pp. 233-241.
    • (1981) Combinatorica , vol.1 , pp. 233-241
    • FÜREDI, Z.1    KOMLOS, J.2
  • 19
    • 0003659644 scopus 로고    scopus 로고
    • Computing on Data Streams
    • Tech. Report 1998-011, Digital Systems Research Center, Palo Alto, CA
    • M. R. HENZINGER, P. RAGHAVAN, AND S. RAJAGOPALAN, Computing on Data Streams, Tech. Report 1998-011, Digital Systems Research Center, Palo Alto, CA, 1998.
    • (1998)
    • HENZINGER, M.R.1    RAGHAVAN, P.2    RAJAGOPALAN, S.3
  • 21
    • 0003713181 scopus 로고    scopus 로고
    • On the Concentration of Eigenvalues of Random Symmetric Matrices
    • Tech. Report MSR-TR-2000-60, Microsoft Research, Redmond, WA
    • M. KRIVELEVICH AND V. H. VU, On the Concentration of Eigenvalues of Random Symmetric Matrices, Tech. Report MSR-TR-2000-60, Microsoft Research, Redmond, WA, 2000.
    • (2000)
    • KRIVELEVICH, M.1    VU, V.H.2
  • 22
    • 0001035413 scopus 로고
    • On the method of bounded differences
    • J. Siemons, ed, London Math. Soc. Lecture Notes Ser, Cambridge University Press, Cambridge, UK
    • C. MCDIARMID, On the method of bounded differences, in Surveys in Combinatorics, 1989, J. Siemons, ed., London Math. Soc. Lecture Notes Ser., Cambridge University Press, Cambridge, UK, 1989, pp. 148-188.
    • (1989) Surveys in Combinatorics, 1989 , pp. 148-188
    • MCDIARMID, C.1
  • 26
    • 34250487811 scopus 로고
    • Gaussian elimination is not optimal
    • V. STRASSEN, Gaussian elimination is not optimal, Numer. Math., 14 (1969), pp. 354-356.
    • (1969) Numer. Math , vol.14 , pp. 354-356
    • STRASSEN, V.1
  • 27
    • 84858533218 scopus 로고    scopus 로고
    • manuscript; available online from
    • n, manuscript; available online from http://arxiv.org/abs/math/0011232.
    • n
    • VERSHYNIN, R.1
  • 28
    • 0022026217 scopus 로고
    • Random sampling with a reservoir
    • J. S. VITTER, Random sampling with a reservoir, ACM Trans. Math. Softw., 11 (1985), pp. 37-57.
    • (1985) ACM Trans. Math. Softw , vol.11 , pp. 37-57
    • VITTER, J.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.