메뉴 건너뛰기




Volumn , Issue , 2005, Pages 117-164

Parallel algorithms for the singular value decomposition

Author keywords

[No Author keywords available]

Indexed keywords


EID: 85057401994     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter
Times cited : (26)

References (109)
  • 1
    • 0002741413 scopus 로고
    • Large scale singular value computations
    • M.W. Berry. Large scale singular value computations. Int. J. Supercomputer Appl., 6:13-49, 1992.
    • (1992) Int. J. Supercomputer Appl , vol.6 , pp. 13-49
    • Berry, M.W.1
  • 2
    • 0004236492 scopus 로고    scopus 로고
    • 3rd ed. Johns Hopkins University Press, Baltimore, MD
    • G.H. Golub and C.F.Van Loan. Matrix Computations, 3rd ed. Johns Hopkins University Press, Baltimore, MD, 1996.
    • (1996) Matrix Computations
    • Golub, G.H.1    van Loan, C.F.2
  • 4
    • 0042913333 scopus 로고    scopus 로고
    • Condition number and backward error for the generalized singular value decomposition
    • J.-G. Sun. Condition number and backward error for the generalized singular value decomposition. SIAMJ. Matrix Anal. Appl., 22(2):323-341, 2000.
    • (2000) SIAMJ. Matrix Anal. Appl , vol.22 , Issue.2 , pp. 323-341
    • Sun, J.-G.1
  • 7
    • 0039569015 scopus 로고
    • A note on simple non-zero singular values
    • J.-G. Sun. A note on simple non-zero singular values. J. Comput. Math., (6):258-266, 1988.
    • (1988) J. Comput. Math , pp. 258-266
    • Sun, J.-G.1
  • 8
    • 0036379361 scopus 로고    scopus 로고
    • Numerical reliability for mixed methods applied to flow problems in porous media
    • H. Hoteit, J. Erhel, R. Mose, B. Philippe, and P. Ackerer. Numerical reliability for mixed methods applied to flow problems in porous media. J. Comput. Geosci., 6:161-194, 2002.
    • (2002) J. Comput. Geosci , vol.6 , pp. 161-194
    • Hoteit, H.1    Erhel, J.2    Mose, R.3    Philippe, B.4    Ackerer, P.5
  • 9
    • 0000992781 scopus 로고
    • Pseudospectra of matrices
    • D.F. Griffiths and G.A. Watson, Eds., Dundee, Longman, Chicago
    • L.N. Trefethen. Pseudospectra of matrices. In D.F. Griffiths and G.A. Watson, Eds., Numerical Analysis, Dundee 1991. Longman, Chicago, 1992, pp. 234-266.
    • (1992) Numerical Analysis , vol.1991 , pp. 234-266
    • Trefethen, L.N.1
  • 10
    • 0041616825 scopus 로고
    • Spectral portraits of matrices and criteria of spectrum dichotomy
    • L. Atanassova and J. Hezberger, Eds., Amsterdam
    • S.K. Godunov. Spectral portraits of matrices and criteria of spectrum dichotomy. In L. Atanassova and J. Hezberger, Eds., 3rd Int. IMACS-CAMM Symp. Comp. Arithmetic Enclosure Meth., Amsterdam, 1992.
    • (1992) 3Rd Int. IMACS-CAMM Symp. Comp. Arithmetic Enclosure Meth
    • Godunov, S.K.1
  • 11
    • 1542498744 scopus 로고    scopus 로고
    • A curve tracing algorithm for computing the pseudospectrum
    • M. Briihl. A curve tracing algorithm for computing the pseudospectrum. BIT, 36(3): 441-454, 1996.
    • (1996) BIT , vol.36 , Issue.3 , pp. 441-454
    • Briihl, M.1
  • 12
    • 0035980882 scopus 로고    scopus 로고
    • Cobra: Parallel path following for computing the matrix pseudospectrum
    • C. Bekas and E. Gallopoulos. Cobra: parallel path following for computing the matrix pseudospectrum. Parallel Comput., 27(14):1879-1896, 2001.
    • (2001) Parallel Comput , vol.27 , Issue.14 , pp. 1879-1896
    • Bekas, C.1    Gallopoulos, E.2
  • 13
    • 0036467555 scopus 로고    scopus 로고
    • Parallel computation of pseudospectra of large sparse matrices
    • D. Mezher and B. Philippe. Parallel computation of pseudospectra of large sparse matrices. Parallel Comput., 28(2):199-221, 2002.
    • (2002) Parallel Comput , vol.28 , Issue.2 , pp. 199-221
    • Mezher, D.1    Philippe, B.2
  • 14
    • 85057357819 scopus 로고    scopus 로고
    • Matrix Market. http://math.nist.gov/MatrixMarket/.
  • 20
    • 85057381217 scopus 로고    scopus 로고
    • Mathtools.net > matlab > parallel
    • Mathtools.net. Mathtools.net > matlab > parallel. http://www.mathtools.net/MATLAB/Parallel/.
  • 21
    • 84967689571 scopus 로고
    • The cyclic jacobi method for computing the principal values of a complex matrix
    • G. Forsythe and P. Henrici. The cyclic Jacobi method for computing the principal values of a complex matrix. Trans. Am. Math. Soc., 94:1-23, 1960.
    • (1960) Trans. Am. Math. Soc , vol.94 , pp. 1-23
    • Forsythe, G.1    Henrici, P.2
  • 22
    • 4243810288 scopus 로고
    • Zur konvergenz des jacobi-verfahrens
    • A. Schonhage. Zur konvergenz des Jacobi-Verfahrens. Numer. Math., 3:374-380, 1961.
    • (1961) Numer. Math , vol.3 , pp. 374-380
    • Schonhage, A.1
  • 23
    • 0039081457 scopus 로고
    • Note on the quadratic convergence of the cyclic jacobi process
    • J.H. Wilkinson. Note on the quadratic convergence of the cyclic jacobi process. Numer. Math., 5: 296-300, 1962.
    • (1962) Numer. Math , vol.5 , pp. 296-300
    • Wilkinson, J.H.1
  • 24
    • 84968513725 scopus 로고
    • On jacobi and jacobi-like algorithms for a parallel computer
    • A. Sameh. On Jacobi and Jacobi-like algorithms for a parallel computer. Math. Comput., 25:579-590, 1971.
    • (1971) Math. Comput , vol.25 , pp. 579-590
    • Sameh, A.1
  • 25
    • 0024680783 scopus 로고
    • A proof of convergence for two parallel jacobi svd algorithms
    • F. Luk and H. Park. A proof of convergence for two parallel Jacobi SVD algorithms. IEEE Trans. Comput., 38(6):806-811, 1989.
    • (1989) IEEE Trans. Comput , vol.38 , Issue.6 , pp. 806-811
    • Luk, F.1    Park, H.2
  • 26
    • 0037783300 scopus 로고
    • On parallel jacobi orderings
    • F. Luk and H. Park. On parallel Jacobi orderings. SIAM J. Sci. Stat. Comput., 10(1):18-26, 1989.
    • (1989) SIAM J. Sci. Stat. Comput , vol.10 , Issue.1 , pp. 18-26
    • Luk, F.1    Park, H.2
  • 27
    • 0040742107 scopus 로고
    • On the speed of convergence of cyclic and quasicyclic jacobi methods for computing eigenvalues of hermitian matrices
    • P. Henrici. On the speed of convergence of cyclic and quasicyclic Jacobi methods for computing eigenvalues of Hermitian matrices. Soc. Ind. Appl. Math., 6:144-162, 1958.
    • (1958) Soc. Ind. Appl. Math , vol.6 , pp. 144-162
    • Henrici, P.1
  • 29
    • 0343087358 scopus 로고
    • The jk method: A procedure for finding the eigenvectors and eigenvalues of a real symmetric matrix
    • H.F. Kaiser. The JK method: a procedure for finding the eigenvectors and eigenvalues of a real symmetric matrix. Comput. J., 15(33):271-273, 1972.
    • (1972) Comput. J , vol.15 , Issue.33 , pp. 271-273
    • Kaiser, H.F.1
  • 30
    • 0016471603 scopus 로고
    • A one-sided transformation method for the singular value decomposition and algebraic eigenproblems
    • J.C. Nash. A one-sided transformation method for the singular value decomposition and algebraic eigenproblems. Comput. J., 18(1):74-76, 1975.
    • (1975) Comput. J , vol.18 , Issue.1 , pp. 74-76
    • Nash, J.C.1
  • 31
    • 84976811521 scopus 로고
    • Computing the singular value decomposition on the illiac iv
    • F.T. Luk. Computing the singular value decomposition on the Illiac IV. ACM Trans. Math. Soft., 6(4):524-539, 1980.
    • (1980) ACM Trans. Math. Soft , vol.6 , Issue.4 , pp. 524-539
    • Luk, F.T.1
  • 32
    • 0002115256 scopus 로고
    • The solution of singular value and symmetric eigenproblems on multiprocessor arrays
    • R.P. Brent and F.T. Luk. The solution of singular value and symmetric eigenproblems on multiprocessor arrays. SIAM J. Sci. Stat., 6:69-84, 1985.
    • (1985) SIAM J. Sci. Stat , vol.6 , pp. 69-84
    • Brent, R.P.1    Luk, F.T.2
  • 33
    • 0021822541 scopus 로고
    • Computation of the singular value decomposition using mesh connected processors
    • R.P. Brent, F.T. Luk, and C. Van Loan. Computation of the singular value decomposition using mesh connected processors. VLSI Comput. Syst., 1(3):242-270, 1985.
    • (1985) VLSI Comput. Syst , vol.1 , Issue.3 , pp. 242-270
    • Brent, R.P.1    Luk, F.T.2    Van Loan, C.3
  • 34
    • 38249005068 scopus 로고
    • An overview of parallel algorithms for the singular value and symmetric eigenvalue problems
    • M.W. Berry and A.H. Sameh. An overview of parallel algorithms for the singular value and symmetric eigenvalue problems. Comput. Appl. Math., 27:191-213, 1989.
    • (1989) Comput. Appl. Math , vol.27 , pp. 191-213
    • Berry, M.W.1    Sameh, A.H.2
  • 35
    • 0000725833 scopus 로고
    • On efficient implementations of kogbetliantz’s algorithm for computing the singular value decomposition
    • J.-P. Charlier, M. Vanbegin, and P. Van Dooren. On efficient implementations of Kogbetliantz’s algorithm for computing the singular value decomposition. Numer. Math., 52:279-300, 1988.
    • (1988) Numer. Math , vol.52 , pp. 279-300
    • Charlier, J.-P.1    Vanbegin, M.2    Van Dooren, P.3
  • 36
    • 0000588703 scopus 로고
    • On the quadratic convergence of kogbetliantz’s algorithm for computing the singular value decomposition
    • C. Paige and P. Van Dooren. On the quadratic convergence of Kogbetliantz’s algorithm for computing the singular value decomposition. Linear Algebra Appl., 77:301-313, 1986.
    • (1986) Linear Algebra Appl , vol.77 , pp. 301-313
    • Paige, C.1    Van Dooren, P.2
  • 37
    • 0000098487 scopus 로고
    • On kogbetliantz’s svd algorithm in the presence of clusters
    • J.-P. Charlier and P. Van Dooren. On Kogbetliantz’s SVD algorithm in the presence of clusters. Linear Algebra Appl., 95:135-160, 1987.
    • (1987) Linear Algebra Appl , vol.95 , pp. 135-160
    • Charlier, J.-P.1    Van Dooren, P.2
  • 38
    • 0040662069 scopus 로고
    • Almost diagonal matrices with multiple or close eigenvalues
    • J.H. Wilkinson. Almost diagonal matrices with multiple or close eigenvalues. Linear Algebra Appl., 1:1-12, 1968.
    • (1968) Linear Algebra Appl , vol.1 , pp. 1-12
    • Wilkinson, J.H.1
  • 39
    • 0007990957 scopus 로고    scopus 로고
    • Block-jacobi svd algorithms for distributed memory systems i
    • M. Becka and M. Vajtesic. Block-Jacobi SVD algorithms for distributed memory systems I. Parallel Algorithms Appl., 13:265-267, 1999.
    • (1999) Parallel Algorithms Appl , vol.13 , pp. 265-267
    • Becka, M.1    Vajtesic, M.2
  • 40
    • 0007990958 scopus 로고    scopus 로고
    • Block-jacobi svd algorithms for distributed memory systems ii
    • M. Becka and M. Vajtesic. Block-Jacobi SVD algorithms for distributed memory systems II. Parallel Algorithms Appl., 14:37-56, 1999.
    • (1999) Parallel Algorithms Appl , vol.14 , pp. 37-56
    • Becka, M.1    Vajtesic, M.2
  • 41
    • 0036467463 scopus 로고    scopus 로고
    • Dynamic ordering for a block-jacobi svd algorithm
    • M. Becka, G. Oksa, and M. Vajtesic. Dynamic ordering for a Block-Jacobi SVD algorithm. Parallel Comput., 28:243-262, 2002.
    • (2002) Parallel Comput , vol.28 , pp. 243-262
    • Becka, M.1    Oksa, G.2    Vajtesic, M.3
  • 44
    • 21344466930 scopus 로고    scopus 로고
    • Multifrontal qr factorization in a multiprocessor environment
    • P.R. Amestoy, I.S. Duff, and C. Puglisi. Multifrontal QR factorization in a multiprocessor environment. Numer. Linear Algebra Appl., 3:275-300, 1996.
    • (1996) Numer. Linear Algebra Appl , vol.3 , pp. 275-300
    • Amestoy, P.R.1    Duff, I.S.2    Puglisi, C.3
  • 45
    • 0033884893 scopus 로고    scopus 로고
    • Multifrontal parallel distributed symmetric and unsymmetric solvers
    • P.R. Amestoy, I.S. Duff, and J.Y. L’Excellent. Multifrontal parallel distributed symmetric and unsymmetric solvers. Comput. Meth. Appl. Mech. Eng., 184(2-4):501-520, 2000.
    • (2000) Comput. Meth. Appl. Mech. Eng , vol.184 , Issue.2-4 , pp. 501-520
    • Amestoy, P.R.1    Duff, I.S.2    L’Excellent, J.Y.3
  • 46
    • 0036398772 scopus 로고    scopus 로고
    • Nested-dissection orderings for sparse lu with partial pivoting
    • I. Brainman and S. Toledo. Nested-dissection orderings for sparse LU with partial pivoting. SIAM J. Matrix Anal. Appl., 23(4):998-1012, 2002.
    • (2002) SIAM J. Matrix Anal. Appl , vol.23 , Issue.4 , pp. 998-1012
    • Brainman, I.1    Toledo, S.2
  • 47
    • 0001946784 scopus 로고    scopus 로고
    • A combined unifrontal/multifrontal method for unsymmetric sparse matrices
    • T.A. Davis and I.S. Duff. A combined unifrontal/multifrontal method for unsymmetric sparse matrices. ACM Trans. Math. Software, 25:1-19, 1999.
    • (1999) ACM Trans. Math. Software , vol.25 , pp. 1-19
    • Davis, T.A.1    Duff, I.S.2
  • 50
    • 0030564734 scopus 로고    scopus 로고
    • A review of frontal methods for solving linear systems
    • I.S. Duff. A review of frontal methods for solving linear systems. Comput. Phys. Commun., 97(1-2):45-52, 1996.
    • (1996) Comput. Phys. Commun , vol.97 , Issue.1-2 , pp. 45-52
    • Duff, I.S.1
  • 51
    • 0042318563 scopus 로고    scopus 로고
    • Computing row and column counts for sparse qr and lu factorization
    • J.R. Gilbert, X.S. Li, E.G. Ng, and B.W. Peyton. Computing row and column counts for sparse QR and LU factorization. BIT, 41(4):693-710, 2001.
    • (2001) BIT , vol.41 , Issue.4 , pp. 693-710
    • Gilbert, J.R.1    Li, X.S.2    Ng, E.G.3    Peyton, B.W.4
  • 53
    • 85057417382 scopus 로고    scopus 로고
    • SuperLU version 2, September 1999
    • X.S. Li. SuperLU version 2. http://www.nersc.gov/xiaoye/SuperLU/, September 1999.
    • Li, X.S.1
  • 59
    • 0016555955 scopus 로고
    • Solution of sparse indefinite systems of linear equations
    • C. Paige and M. Saunders. Solution of sparse indefinite systems of linear equations. SIAM J Numeri. Anal., 12:617-629, 1975.
    • (1975) SIAM J Numeri. Anal , vol.12 , pp. 617-629
    • Paige, C.1    Saunders, M.2
  • 60
    • 0000048673 scopus 로고
    • Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Y. Saad and H. Schultz. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7:856-869, 1986.
    • (1986) SIAM J. Sci. Stat. Comput , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, H.2
  • 61
    • 0000005482 scopus 로고
    • Bi-cgstab: A fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems
    • H.A. van der Vorst. Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Statist. Comput., 13:631-644, 1992.
    • (1992) SIAM J. Sci. Statist. Comput , vol.13 , pp. 631-644
    • Van Der Vorst, H.A.1
  • 62
    • 25444452938 scopus 로고
    • Qmr: A quasi-minimal residual method for non-hermitian linear systems
    • R. Freund and N. Nachtigal. QMR: a quasi-minimal residual method for non-Hermitian linear systems. Numer. Math., 60:315-339, 1991.
    • (1991) Numer. Math , vol.60 , pp. 315-339
    • Freund, R.1    Nachtigal, N.2
  • 63
    • 0001031880 scopus 로고
    • A transpose-free quasi-minimal residual algorithm for non-hermitian linear systems
    • R. Freund. A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems. SIAM J. Sci. comput., 14:470-482, 1993.
    • (1993) SIAM J. Sci. Comput , vol.14 , pp. 470-482
    • Freund, R.1
  • 64
    • 0000288016 scopus 로고
    • Calculating the singular values and pseudo-inverse of a matrix
    • G.H. Golub and W. Kahan. Calculating the singular values and pseudo-inverse of a matrix. SIAM J. Numer. Anal., 2(3):205-224, 1965.
    • (1965) SIAM J. Numer. Anal , vol.2 , Issue.3 , pp. 205-224
    • Golub, G.H.1    Kahan, W.2
  • 66
    • 0003027926 scopus 로고
    • Inversion of matrices by biorthogonalization and related results
    • M.R. Hestens. Inversion of matrices by biorthogonalization and related results. Soc. Ind. Appl. Math., 6:51-90, 1958.
    • (1958) Soc. Ind. Appl. Math , vol.6 , pp. 51-90
    • Hestens, M.R.1
  • 68
    • 0000482693 scopus 로고
    • Das verfahred der treppeniteration und verwandte verfahren zur losung algebraischer eigenwertprobleme
    • F.L. Bauer. Das verfahred der treppeniteration und verwandte verfahren zur losung algebraischer eigenwertprobleme. ZAMP, 8:214-235, 1957.
    • (1957) ZAMP , vol.8 , pp. 214-235
    • Bauer, F.L.1
  • 69
    • 0000281504 scopus 로고
    • Simultaneous iteration method for symmetric matrices
    • H. Rutishauser. Simultaneous iteration method for symmetric matrices. Numer. Math., 16:205-223, 1970.
    • (1970) Numer. Math , vol.16 , pp. 205-223
    • Rutishauser, H.1
  • 70
    • 0003272915 scopus 로고
    • The use of blas3 in linear algebra on a parallel processor with a hierarchical memory
    • K. Gallivan, W. Jalby, and U. Meier. The use of BLAS3 in linear algebra on a parallel processor with a hierarchical memory. SIAM J. Sci. Stat. Comput., 18(6):1079-1084, 1987.
    • (1987) SIAM J. Sci. Stat. Comput , vol.18 , Issue.6 , pp. 1079-1084
    • Gallivan, K.1    Jalby, W.2    Meier, U.3
  • 71
    • 0002198379 scopus 로고
    • Computational aspects of f.L. Bauer’s simultaneous iteration method
    • H. Rutishauser. Computational aspects of F.L. Bauer’s simultaneous iteration method. Numer. Math., 13:4-13, 1969.
    • (1969) Numer. Math , vol.13 , pp. 4-13
    • Rutishauser, H.1
  • 73
    • 0000417182 scopus 로고
    • A fast algorithm for the symmetric eigenvalue problem
    • J. Dongarra and D. Sorensen. A fast algorithm for the symmetric eigenvalue problem. SIAM J. Sci. Stat. Comput., 8(2):s139-s154, 1987.
    • (1987) SIAM J. Sci. Stat. Comput , vol.8 , Issue.2 , pp. s139-s154
    • Dongarra, J.1    Sorensen, D.2
  • 74
    • 53849148874 scopus 로고
    • Error analysis of the lanczos algorithms for tridiagonalizing a symmetric matrix
    • C.C. Paige. Error analysis of the Lanczos algorithms for tridiagonalizing a symmetric matrix. Inst. Math. Appl., 18:341-349, 1976.
    • (1976) Inst. Math. Appl , vol.18 , pp. 341-349
    • Paige, C.C.1
  • 76
    • 84968487118 scopus 로고
    • The lanczos algorithm with selective reorthogonalization
    • B.N. Parlett and D.S. Scott. The Lanczos algorithm with selective reorthogonalization. Math. Comput., 33:217-238, 1979.
    • (1979) Math. Comput , vol.33 , pp. 217-238
    • Parlett, B.N.1    Scott, D.S.2
  • 77
    • 0000682936 scopus 로고
    • Analysis of the symmetric lanczos algorithm with reorthogonalization methods
    • H. Simon. Analysis of the symmetric Lanczos algorithm with reorthogonalization methods. Linear Algebra Appl., 61:101-131, 1984.
    • (1984) Linear Algebra Appl , vol.61 , pp. 101-131
    • Simon, H.1
  • 78
    • 0002931065 scopus 로고
    • A multiprocessor algorithm for the symmetric tridiagonal eigenvalue problem
    • S. Lo, B. Philippe, and A.H. Sameh. A multiprocessor algorithm for the symmetric tridiagonal eigenvalue problem. SIAM J. Sci. Stat. Comput., 8(2):s155-s165, 1987.
    • (1987) SIAM J. Sci. Stat. Comput , vol.8 , Issue.2 , pp. s155-s165
    • Lo, S.1    Philippe, B.2    Sameh, A.H.3
  • 79
    • 0004236492 scopus 로고    scopus 로고
    • 2nd ed. Johns Hopkins University Press, Battimore, MD
    • G.H. Golub and C. Van Loan. Matrix Computations, 2nd ed. Johns Hopkins University Press, Battimore, MD, 1989.
    • (1989) Matrix Computations
    • Golub, G.H.1    Van Loan, C.2
  • 82
    • 0019576431 scopus 로고
    • A block lanczos method for computing the singular values and corresponding singular vectors of amatrix
    • G.H. Golub, F.T. Luk, and M.L. Overton. A block Lanczos method for computing the singular values and corresponding singular vectors of amatrix. ACM Trans. Math. Software, 7(2):149-169, 1981.
    • (1981) ACM Trans. Math. Software , vol.7 , Issue.2 , pp. 149-169
    • Golub, G.H.1    Luk, F.T.2    Overton, M.L.3
  • 84
    • 0001065610 scopus 로고
    • Stability analysis and improvement of the block gram-schmidt algorithm
    • W. Jalby and B. Philippe. Stability analysis and improvement of the block Gram-Schmidt algorithm. SIAMJ. Sci. Stat. Comput., 12(5):1058-1073, 1991.
    • (1991) SIAMJ. Sci. Stat. Comput , vol.12 , Issue.5 , pp. 1058-1073
    • Jalby, W.1    Philippe, B.2
  • 85
    • 0009148594 scopus 로고
    • A trace minimization algorithm for the generalized eigenvalue problem
    • A.H. Sameh and J.A. Wisniewski. A trace minimization algorithm for the generalized eigenvalue problem. SIAM J. Numer. Anal., 19(6):1243-1259, 1982.
    • (1982) SIAM J. Numer. Anal , vol.19 , Issue.6 , pp. 1243-1259
    • Sameh, A.H.1    Wisniewski, J.A.2
  • 87
    • 85057434219 scopus 로고
    • Computing extremal singular triplets of sparse matrices on a shared-memory multiprocessor
    • M.W. Berry, B. Parlett, and A.H. Sameh. Computing extremal singular triplets of sparse matrices on a shared-memory multiprocessor. Int. J. High Speed Comput., 2:239-275, 1994.
    • (1994) Int. J. High Speed Comput , vol.2 , pp. 239-275
    • Berry, M.W.1    Parlett, B.2    Sameh, A.H.3
  • 90
    • 1542379944 scopus 로고    scopus 로고
    • Computing smallest singular triplets with implicitly restarted lanczos bidiagonalization
    • E. Kokiopoulou, C. Bekas, and E. Gallopoulos. Computing Smallest Singular Triplets with Implicitly Restarted Lanczos Bidiagonalization. J. Appl. Numer., 49(1):39-61, 2004.
    • (2004) J. Appl. Numer , vol.49 , Issue.1 , pp. 39-61
    • Kokiopoulou, E.1    Bekas, C.2    Gallopoulos, E.3
  • 91
    • 0001287220 scopus 로고
    • On the reduction of a symmetric matrix to tridiagonal form
    • J.O. Aasen. On the reduction of a symmetric matrix to tridiagonal form. BIT, 11:233-242, 1971.
    • (1971) BIT , vol.11 , pp. 233-242
    • Aasen, J.O.1
  • 92
    • 84966228742 scopus 로고
    • Some stable methods for calculating inertia and solving symmetric linear systems
    • J.R. Bunch and L. Kaufman. Some stable methods for calculating inertia and solving symmetric linear systems. Math. Comput., 31:162-179, 1977.
    • (1977) Math. Comput , vol.31 , pp. 162-179
    • Bunch, J.R.1    Kaufman, L.2
  • 93
    • 0009152793 scopus 로고
    • On the solution of a system of linear equations whose system is symmetric but not definite
    • B.N. Parlett and J.K. Reid. On the solution of a system of linear equations whose system is symmetric but not definite. BIT, 10:386-397, 1970.
    • (1970) BIT , vol.10 , pp. 386-397
    • Parlett, B.N.1    Reid, J.K.2
  • 94
    • 0016555955 scopus 로고
    • Solution of sparse indefinite systems of linear equations
    • C.C. Paige and M.A. Saunders. Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal., 12(4):617-629, 1975.
    • (1975) SIAM J. Numer. Anal , vol.12 , Issue.4 , pp. 617-629
    • Paige, C.C.1    Saunders, M.A.2
  • 95
    • 5344230920 scopus 로고
    • The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
    • E.R. Davidson. The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices. Comput. Phys., 17:87-94, 1975.
    • (1975) Comput. Phys , vol.17 , pp. 87-94
    • Davidson, E.R.1
  • 96
    • 0001398614 scopus 로고
    • Generalizations of davidson’s method for computing eigenvalues of sparse symmetric matrices
    • R.B. Morgan and D.S. Scott. Generalizations of Davidson’s method for computing eigenvalues of sparse symmetric matrices. SIAM J. Sci. Stat. Comput., 7:817-825, 1986.
    • (1986) SIAM J. Sci. Stat. Comput , vol.7 , pp. 817-825
    • Morgan, R.B.1    Scott, D.S.2
  • 98
    • 0030560293 scopus 로고    scopus 로고
    • A jacobi-davidson iteration method for linear eigenvalue problems
    • Also SIGEST inSIAM Rev. 42(2): 267-293
    • G.L.G. Sleipen and H.A. van der Vorst. A Jacobi-Davidson iteration method for linear eigenvalue problems. SIAM J. Matrix Anal. Appl., 17(2):401-425, 1996. Also SIGEST in SIAM Rev. 42(2): 267-293.
    • (1996) SIAM J. Matrix Anal. Appl , vol.17 , Issue.2 , pp. 401-425
    • Sleipen, G.L.G.1    Van Der Vorst, H.A.2
  • 99
    • 0034319898 scopus 로고    scopus 로고
    • The trace minimization method for the symmetric generalized eigenvalue problem
    • A. Sameh and Z. Tong. The trace minimization method for the symmetric generalized eigenvalue problem. J. Comput. Appl. Math., 123:155-175, 2000.
    • (2000) J. Comput. Appl. Math , vol.123 , pp. 155-175
    • Sameh, A.1    Tong, Z.2
  • 100
    • 0009924727 scopus 로고    scopus 로고
    • Inexact rayleigh quotient-type methods for eigenvalue computations
    • V. Simoncini and L. Elden. Inexact Rayleigh quotient-type methods for eigenvalue computations. BIT, 42(1):159-182, 2002.
    • (2002) BIT , vol.42 , Issue.1 , pp. 159-182
    • Simoncini, V.1    Elden, L.2
  • 101
    • 0040514637 scopus 로고    scopus 로고
    • Computation of the fundamental singular subspace of a large matrix
    • B. Philippe and M. Sadkane. Computation of the fundamental singular subspace of a large matrix. Linear Algebra Appl., 257:77-104, 1997.
    • (1997) Linear Algebra Appl , vol.257 , pp. 77-104
    • Philippe, B.1    Sadkane, M.2
  • 102
    • 0036222763 scopus 로고    scopus 로고
    • A jacobi-davidson type svd method
    • M.E. Hochstenbach. A Jacobi-Davidson type SVD method. SIAM J. Sci. Comput., 23(2):606-628, 2001.
    • (2001) SIAM J. Sci. Comput , vol.23 , Issue.2 , pp. 606-628
    • Hochstenbach, M.E.1
  • 103
    • 0043234058 scopus 로고    scopus 로고
    • Parallel computation of spectral portrait of large matrices by davidson type methods
    • V. Heuveline, B. Philippe, and M. Sadkane. Parallel computation of spectral portrait of large matrices by Davidson type methods. Numer. Algorithms, 16(1):55-75, 1997.
    • (1997) Numer. Algorithms , vol.16 , Issue.1 , pp. 55-75
    • Heuveline, V.1    Philippe, B.2    Sadkane, M.3
  • 104
    • 84898855093 scopus 로고
    • Parallel krylov subspace basis computation
    • J. Tankoano, Ed., INRIA - ORSTOM, ORSTOM Editions, Paris
    • R. Sidje and B. Philippe. Parallel Krylov subspace basis computation. In J. Tankoano, Ed., CARI’94 Proc., Ouagadougou. INRIA - ORSTOM, ORSTOM Editions, Paris, 1994, pp. 421-440.
    • (1994) CARI’94 Proc., Ouagadougou , pp. 421-440
    • Sidje, R.1    Philippe, B.2
  • 105
    • 21344466930 scopus 로고    scopus 로고
    • Multifrontal qr factorization in a multiprocessor environment
    • P.R. Amestoy, I.S. Duff, and C. Puglisi. Multifrontal QR factorization in a multiprocessor environment. Numer. Linear Algebra Appl., 3:275-300, 1996.
    • (1996) Numer. Linear Algebra Appl , vol.3 , pp. 275-300
    • Amestoy, P.R.1    Duff, I.S.2    Puglisi, C.3
  • 106
    • 85011519633 scopus 로고    scopus 로고
    • Computation of pseudospectra
    • L.N. Trefethen. Computation of pseudospectra. Acta Numer., 8:247-295, 1999.
    • (1999) Acta Numer , vol.8 , pp. 247-295
    • Trefethen, L.N.1
  • 107
    • 0031082730 scopus 로고    scopus 로고
    • Computation of pseudospectra by continuation
    • S.H. Lui. Computation of pseudospectra by continuation. SIAM J. Sci. Comput., 28(2): 565-573, 1997.
    • (1997) SIAM J. Sci. Comput , vol.28 , Issue.2 , pp. 565-573
    • Lui, S.H.1
  • 109
    • 0036248978 scopus 로고    scopus 로고
    • Pat - a reliable path-following algorithm
    • D. Mezher and B. Philippe. PAT - a reliable path-following algorithm. Numer. Algorithms, 29: 131-152, 2002.
    • (2002) Numer. Algorithms , vol.29 , pp. 131-152
    • Mezher, D.1    Philippe, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.