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Volumn 37, Issue 12, 2011, Pages 795-805

MR3-SMP: A symmetric tridiagonal eigensolver for multi-core architectures

Author keywords

Eigenvalue; Eigenvector; MRRR algorithm; Multi core; Tridiagonal eigensolver

Indexed keywords

DISTRIBUTED MEMORY; DISTRIBUTED MEMORY SYSTEMS; EIGEN-PROBLEMS; EIGEN-VALUE; EIGENPROBLEM; EIGENSOLVERS; EIGENVALUES AND EIGENVECTORS; GENERAL PURPOSE PROCESSORS; HERMITIANS; MANY-CORE; MULTI CORE; MULTICORE ARCHITECTURES; TRIDIAGONAL; TRIDIAGONAL MATRICES;

EID: 81355146342     PISSN: 01678191     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.parco.2011.10.001     Document Type: Conference Paper
Times cited : (8)

References (30)
  • 2
    • 2942522546 scopus 로고    scopus 로고
    • Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices
    • I. Dhillon, and B. Parlett Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices Linear Algebra Appl. 387 2004 1 28
    • (2004) Linear Algebra Appl. , vol.387 , pp. 1-28
    • Dhillon, I.1    Parlett, B.2
  • 4
    • 55549110811 scopus 로고    scopus 로고
    • Performance and accuracy of LAPACK's symmetric tridiagonal eigensolvers
    • J. Demmel, O. Marques, B. Parlett, and C. Voemel Performance and accuracy of LAPACK's symmetric tridiagonal eigensolvers SIAM J. Sci. Comput. 30 2008 1508 1526
    • (2008) SIAM J. Sci. Comput. , vol.30 , pp. 1508-1526
    • Demmel, J.1    Marques, O.2    Parlett, B.3    Voemel, C.4
  • 7
    • 33144474872 scopus 로고    scopus 로고
    • A parallel eigensolver for dense symmetric matrices based on multiple relatively robust representations
    • DOI 10.1137/030601107
    • P. Bientinesi, I. Dhillon, and R. van de Geijn A parallel eigensolver for dense symmetric matrices based on multiple relatively robust representations SIAM J. Sci. Comput. 21 2005 43 66 (Pubitemid 43268526)
    • (2005) SIAM Journal of Scientific Computing , vol.27 , Issue.1 , pp. 43-66
    • Bientinesi, P.1    Dhillon, I.S.2    Van Geijn, R.A.D.E.3
  • 15
    • 0012730035 scopus 로고
    • The calculation of the eigenvectors of codiagonal matrices
    • J. Wilkinson The calculation of the eigenvectors of codiagonal matrices Comput. J. 1 1958 90 96
    • (1958) Comput. J. , vol.1 , pp. 90-96
    • Wilkinson, J.1
  • 16
    • 0000394779 scopus 로고
    • The QR transform - A unitary analogue to the LR transformation, Part i and II
    • J. Francis, The QR transform - a unitary analogue to the LR transformation, Part I and II, Comput. J. 4 (1961/1962).
    • (1961) Comput. J. , pp. 4
    • Francis, J.1
  • 17
    • 0039966628 scopus 로고
    • On some algorithms for the solution of the complete eigenvalue problem
    • V. Kublanovskaya On some algorithms for the solution of the complete eigenvalue problem Zh. Vych. Mat. 1 1961 555 572
    • (1961) Zh. Vych. Mat. , vol.1 , pp. 555-572
    • Kublanovskaya, V.1
  • 18
    • 0000659575 scopus 로고
    • A divide and conquer method for the symmetric tridiagonal eigenproblem
    • J. Cuppen A divide and conquer method for the symmetric tridiagonal eigenproblem Numer. Math. 36 1981 177 195
    • (1981) Numer. Math. , vol.36 , pp. 177-195
    • Cuppen, J.1
  • 19
    • 21844526695 scopus 로고
    • A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem
    • M. Gu, and S.C. Eisenstat A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem SIAM J. Matrix Anal. Appl. 16 1995 172 191
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 172-191
    • Gu, M.1    Eisenstat, S.C.2
  • 20
    • 0033293693 scopus 로고    scopus 로고
    • Parallelizing the divide and conquer algorithm for the symmetric tridiagonal eigenvalue problem on distributed memory architectures
    • F. Tisseur, J. Dongarra, and J. Dongarra Parallelizing the divide and conquer algorithm for the symmetric tridiagonal eigenvalue problem on distributed memory architectures SIAM J. Sci. Comput. 20 1998 2223 2236
    • (1998) SIAM J. Sci. Comput. , vol.20 , pp. 2223-2236
    • Tisseur, F.1    Dongarra, J.2    Dongarra, J.3
  • 21
    • 0002931065 scopus 로고
    • A multiprocessor algorithm for the symmetric tridiagonal eigenvalue problem
    • S.-S. Lo, B. Philippe, and A. Sameh A multiprocessor algorithm for the symmetric tridiagonal eigenvalue problem SIAM J. Sci. Stat. Comput. 8 1987 155 165
    • (1987) SIAM J. Sci. Stat. Comput. , vol.8 , pp. 155-165
    • Lo, S.-S.1    Philippe, B.2    Sameh, A.3
  • 22
    • 0041544728 scopus 로고
    • Solving the symmetric tridiagonal eigenvalues problem on the hypercube
    • L.C.F. Ipsen, and E.R. Jessup Solving the symmetric tridiagonal eigenvalues problem on the hypercube SIAM J. Sci. Stat. Comput. 11 1990 203 229
    • (1990) SIAM J. Sci. Stat. Comput. , vol.11 , pp. 203-229
    • Ipsen, L.C.F.1    Jessup, E.R.2
  • 23
    • 0034421232 scopus 로고    scopus 로고
    • Relatively robust representations of symmetric tridiagonals
    • B. Parlett, and I. Dhillon Relatively robust representations of symmetric tridiagonals Linear Algebra Appl. 309 1999 121 151
    • (1999) Linear Algebra Appl. , vol.309 , pp. 121-151
    • Parlett, B.1    Dhillon, I.2
  • 24
    • 0001015596 scopus 로고
    • On the correctness of some bisection-like parallel eigenvalue algorithms in floating point arithmetic
    • J. Demmel, I. Dhillon, and H. Ren On the correctness of some bisection-like parallel eigenvalue algorithms in floating point arithmetic Electronic Trans. Numer. Anal. 3 1995 116 149
    • (1995) Electronic Trans. Numer. Anal. , vol.3 , pp. 116-149
    • Demmel, J.1    Dhillon, I.2    Ren, H.3
  • 25
    • 0022602354 scopus 로고
    • Parallel implementation of bisection for the calculation of eigenvalues of tridiagonal symmetric matrices
    • H. Bernstein, and M. Goldstein Parallel implementation of bisection for the calculation of eigenvalues of tridiagonal symmetric matrices Computing 37 1986 85 91 (Pubitemid 16611891)
    • (1986) Computing (Vienna/New York) , vol.37 , Issue.1 , pp. 85-91
    • Bernstein, H.J.1    Goldstein, M.2
  • 26
    • 0034379502 scopus 로고    scopus 로고
    • An implementation of the DQDS algorithm (positive case)
    • B. Parlett, and O. Marques An implementation of the DQDS algorithm (positive case) Linear Algebra Appl. 309 1999 217 259
    • (1999) Linear Algebra Appl. , vol.309 , pp. 217-259
    • Parlett, B.1    Marques, O.2
  • 27
    • 0010843126 scopus 로고
    • Der quotienten-differenzen-algorithmus
    • H. Rutishauser Der quotienten-differenzen-algorithmus Z. Angew. Math. Phys. 5 1954 223 251
    • (1954) Z. Angew. Math. Phys. , vol.5 , pp. 223-251
    • Rutishauser, H.1
  • 30
    • 48849105175 scopus 로고    scopus 로고
    • Algorithm 880: A testing infrastructure for symmetric tridiagonal eigensolvers
    • O. Marques, C. Voemel, J. Demmel, and B. Parlett Algorithm 880: a testing infrastructure for symmetric tridiagonal eigensolvers ACM Trans. Math. Software 35 2008
    • (2008) ACM Trans. Math. Software , vol.35
    • Marques, O.1    Voemel, C.2    Demmel, J.3    Parlett, B.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.