메뉴 건너뛰기




Volumn 28, Issue 1, 2002, Pages 45-58

An extension of the divide-and-conquer method for a class of symmetric block-tridiagonal eigenproblems

Author keywords

G.1.3 Numerical Analysis : Numerical Linear Algebra Eigenvalues and eigenvectors (direct and iterative methods); G.4 Mathematical Software : Algorithm design and analysis

Indexed keywords


EID: 0040668385     PISSN: 00983500     EISSN: None     Source Type: Journal    
DOI: 10.1145/513001.513004     Document Type: Article
Times cited : (19)

References (27)
  • 2
    • 0026931028 scopus 로고
    • Divide and conquer algorithms for the bandsymmetric eigenvalue problem
    • ARBENZ, P. 1992. Divide and conquer algorithms for the bandsymmetric eigenvalue problem. Parallel Comput. 18, 1105-1128.
    • (1992) Parallel Comput. , vol.18 , pp. 1105-1128
    • Arbenz, P.1
  • 3
    • 0012103078 scopus 로고
    • Restricted rank modification of the symmetric eigenvalue problem: Theoretical considerations
    • ARBENZ, P., GANDER, W., AND GOLUB, G. H. 1988. Restricted rank modification of the symmetric eigenvalue problem: Theoretical considerations. Linear Algebra Appl. 104, 75-95.
    • (1988) Linear Algebra Appl. , vol.104 , pp. 75-95
    • Arbenz, P.1    Gander, W.2    Golub, G.H.3
  • 4
    • 0002931349 scopus 로고
    • On the spectral decomposition of Hermitian matrices modified by low rank perturbations with applications
    • ARBENZ, P. AND GOLUB, G. H. 1988. On the spectral decomposition of Hermitian matrices modified by low rank perturbations with applications. SIAM J. Matrix Anal. Appl. 9, 40-58.
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , pp. 40-58
    • Arbenz, P.1    Golub, G.H.2
  • 5
    • 21144463329 scopus 로고
    • Error analysis of update methods for the symmetric eigenvalue problem
    • BARLOW, J. L. 1993. Error analysis of update methods for the symmetric eigenvalue problem. SIAM J. Matrix Anal. Appl. 14, 598-618.
    • (1993) SIAM J. Matrix Anal. Appl. , vol.14 , pp. 598-618
    • Barlow, J.L.1
  • 6
    • 0002316189 scopus 로고
    • Rank-one modification of the symmetric eigenproblem
    • BUNCH, J. R., NIELSEN, C. P., AND SORENSEN, D. C. 1978. Rank-one modification of the symmetric eigenproblem. Numer. Math. 31, 31-48.
    • (1978) Numer. Math. , vol.31 , pp. 31-48
    • Bunch, J.R.1    Nielsen, C.P.2    Sorensen, D.C.3
  • 7
    • 0000659575 scopus 로고
    • A divide and conquer method for the symmetric tridiagonal eigenproblem
    • CUPPEN, J. J. M. 1981. A divide and conquer method for the symmetric tridiagonal eigenproblem. Numer. Math. 36, 177-195.
    • (1981) Numer. Math. , vol.36 , pp. 177-195
    • Cuppen, J.J.M.1
  • 9
    • 0000417182 scopus 로고
    • A fully parallel algorithm for the symmetric eigenproblem
    • DONGARRA, J. J. AND SORENSEN, D. C. 1987. A fully parallel algorithm for the symmetric eigenproblem. SIAM J. Sci. Comput. 8, s139-s154.
    • (1987) SIAM J. Sci. Comput. , vol.8
    • Dongarra, J.J.1    Sorensen, D.C.2
  • 11
    • 0040609750 scopus 로고    scopus 로고
    • A low-complexity divide-and-conquer method for computing eigenvalues and eigenvectors of symmetric band matrices
    • GANSTERER, W. N., SCHNEID, J., AND UEBERHUBER, C. W. 2001. A low-complexity divide-and-conquer method for computing eigenvalues and eigenvectors of symmetric band matrices. BIT 41, 967-976.
    • (2001) BIT , vol.41 , pp. 967-976
    • Gansterer, W.N.1    Schneid, J.2    Ueberhuber, C.W.3
  • 14
    • 0001070999 scopus 로고
    • Some modified matrix eigenvalue problems
    • GOLUB, G. H. 1973. Some modified matrix eigenvalue problems. SIAM Rev. 15, 318-334.
    • (1973) SIAM Rev. , vol.15 , pp. 318-334
    • Golub, G.H.1
  • 16
    • 21844525426 scopus 로고
    • A stable and efficient algorithm for the rank-one modification of the symmetric eigenproblem
    • GU, M. AND EISENSTAT, S. C. 1994. A stable and efficient algorithm for the rank-one modification of the symmetric eigenproblem. SIAM J. Matrix Anal. Appl. 15, 1266-1276.
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , pp. 1266-1276
    • Gu, M.1    Eisenstat, S.C.2
  • 17
    • 21844526695 scopus 로고
    • A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem
    • GU, M. AND EISENSTAT, S. C. 1995. A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem. SIAM J. Matrix Anal. Appl. 16, 172-191.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 172-191
    • Gu, M.1    Eisenstat, S.C.2
  • 18
    • 0013137925 scopus 로고
    • Solving the secular equations stably and efficiently
    • University of California at Berkeley, Berkeley, CA. Nov.
    • LI, R.-C. 1994. Solving the secular equations stably and efficiently. LAPACK Working Note 89, University of California at Berkeley, Berkeley, CA. Nov.
    • (1994) LAPACK Working Note , vol.89
    • Li, R.-C.1
  • 20
    • 36849100805 scopus 로고
    • Approximate self-consistent molecular orbital theory. V. Intermediate neglect of differential overlap
    • POPLE, J. A., BEVERIDGE, D. L., AND DOBOSH, P. A. 1967. Approximate self-consistent molecular orbital theory. V. Intermediate neglect of differential overlap. J. Chem. Physics 47, 2026.
    • (1967) J. Chem. Physics , vol.47 , pp. 2026
    • Pople, J.A.1    Beveridge, D.L.2    Dobosh, P.A.3
  • 21
    • 36849120328 scopus 로고
    • Approximate self-consistent molecular orbital theory. I. Invariant procedures
    • POPLE, J. A., SANTRY, D. P., AND SEGAL, G. A. 1965. Approximate self-consistent molecular orbital theory. I. Invariant procedures. J. Chem. Physics 43, S129.
    • (1965) J. Chem. Physics , vol.43
    • Pople, J.A.1    Santry, D.P.2    Segal, G.A.3
  • 22
    • 36849116605 scopus 로고
    • Approximate self-consistent molecular orbital theory. II. Calculations with complete neglect of differential overlap
    • POPLE, J. A. AND SEGAL, G. A. 1965. Approximate self-consistent molecular orbital theory. II. Calculations with complete neglect of differential overlap. J. Chem. Physics 43, S136.
    • (1965) J. Chem. Physics , vol.43
    • Pople, J.A.1    Segal, G.A.2
  • 23
    • 36849103011 scopus 로고
    • Approximate self-consistent molecular orbital theory. III. Cndo results for ab2 and ab3 systems
    • POPLE, J. A. AND SEGAL, G. A. 1966. Approximate self-consistent molecular orbital theory. III. CNDO results for ab2 and ab3 systems. J. Chem. Physics 44, 3289.
    • (1966) J. Chem. Physics , vol.44 , pp. 3289
    • Pople, J.A.1    Segal, G.A.2
  • 24
    • 0039424334 scopus 로고
    • A serial implementation of Cuppen's divide and conquer algorithm for the symmetric eigenvalue problem
    • Computer Science Division (EECS), University of California at Berkeley, Berkeley, CA
    • RUTTER, J. 1994. A serial implementation of Cuppen's divide and conquer algorithm for the symmetric eigenvalue problem. LAPACK Working Note 69, Computer Science Division (EECS), University of California at Berkeley, Berkeley, CA.
    • (1994) LAPACK Working Note , vol.69
    • Rutter, J.1
  • 25
    • 0026402822 scopus 로고
    • On the orthogonality of eigenvectors computed by divide-and-conquer techniques
    • SORENSEN, D. C. AND TANG, P. T. P. 1991. On the orthogonality of eigenvectors computed by divide-and-conquer techniques. SIAM J. Numer. Anal. 28, 1752-1775.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 1752-1775
    • Sorensen, D.C.1    Tang, P.T.P.2
  • 27
    • 0033293693 scopus 로고    scopus 로고
    • A parallel divide and conquer algorithm for the symmetric eigenvalue problem on distributed memory architectures
    • TISSEUR, F. AND DONGARRA, J. J. 1999. A parallel divide and conquer algorithm for the symmetric eigenvalue problem on distributed memory architectures. SIAM J. Sci. Comput. 20, 2223-2236.
    • (1999) SIAM J. Sci. Comput. , vol.20 , pp. 2223-2236
    • Tisseur, F.1    Dongarra, J.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.