메뉴 건너뛰기




Volumn 27, Issue 1, 2006, Pages 176-197

An orthogonal similarity reduction of a matrix into semiseparable form

Author keywords

Lanczos algorithm; Ritz values; Semiseparable matrix; Similarity transformation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; ITERATIVE METHODS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL ANALYSIS;

EID: 33144489927     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479803428229     Document Type: Article
Times cited : (19)

References (25)
  • 1
    • 0030194371 scopus 로고    scopus 로고
    • An efficient Chebyshev Lanczos method for obtaining eigensolutions of the Schrödinger equation on a grid
    • M. BRAUN, S. A. SOFIANOS, D. G. PAPAGEORGIOU, AND I. E. LAGARIS, An efficient Chebyshev Lanczos method for obtaining eigensolutions of the Schrödinger equation on a grid, J. Comput. Phys., 126 (1996), pp. 315-327.
    • (1996) J. Comput. Phys. , vol.126 , pp. 315-327
    • Braun, M.1    Sofianos, S.A.2    Papageorgiou, D.G.3    Lagaris, I.E.4
  • 2
    • 0034394306 scopus 로고    scopus 로고
    • Fast and stable eigendecomposition of symmetric banded plus semi-separable matrices
    • S. CHANDRASEKARAN AND M. GU, Fast and stable eigendecomposition of symmetric banded plus semi-separable matrices, Linear Algebra Appl., 313 (2000), pp. 107-114.
    • (2000) Linear Algebra Appl. , vol.313 , pp. 107-114
    • Chandrasekaran, S.1    Gu, M.2
  • 3
    • 1542403825 scopus 로고    scopus 로고
    • A divide and conquer algorithm for the eigendecomposition of symmetric block-diagonal plus semi-separable matrices
    • S. CHANDRASEKARAN AND M. GU, A divide and conquer algorithm for the eigendecomposition of symmetric block-diagonal plus semi-separable matrices, Numer. Math., 96 (2004), pp. 723-731.
    • (2004) Numer. Math. , vol.96 , pp. 723-731
    • Chandrasekaran, S.1    Gu, M.2
  • 4
    • 21144468781 scopus 로고
    • Jacobi's method is more accurate than QR
    • J. DEMMEL AND K. VESELIĆ, Jacobi's method is more accurate than QR, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 1204-1245.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 1204-1245
    • Demmel, J.1    Veselić, K.2
  • 6
    • 20344372250 scopus 로고    scopus 로고
    • Fast and stable algorithms for reducing diagonal plus semiseparable matrices to tridiagonal and bidiagonal form
    • Fast Algorithms for Structured Matrices: Theory and Applications, V. Olshevsky, ed., AMS, Providence, RI, SIAM, Philadelphia
    • D. FASINO, N. MASTRONARDI, AND M. VAN BAREL, Fast and stable algorithms for reducing diagonal plus semiseparable matrices to tridiagonal and bidiagonal form, in Fast Algorithms for Structured Matrices: Theory and Applications, V. Olshevsky, ed., Contemp. Math. 323, AMS, Providence, RI, SIAM, Philadelphia, 2003, pp. 105-118.
    • (2003) Contemp. Math. , vol.323 , pp. 105-118
    • Fasino, D.1    Mastronardi, N.2    Van Barel, M.3
  • 9
    • 0030502142 scopus 로고    scopus 로고
    • Deflation techniques for an implicitly restarted Arnoldi iteration
    • R. B. LEHOUCQ AND D. C. SORENSEN, Deflation techniques for an implicitly restarted Arnoldi iteration, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 789-821.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 789-821
    • Lehoucq, R.B.1    Sorensen, D.C.2
  • 10
    • 0000536720 scopus 로고
    • Householder's tridiagonalization of a symmetric matrix
    • R. S. MARTIN AND J. H. WILKINSON, Householder's tridiagonalization of a symmetric matrix, Numer. Math., 11 (1968), pp. 181-195.
    • (1968) Numer. Math. , vol.11 , pp. 181-195
    • Martin, R.S.1    Wilkinson, J.H.2
  • 11
    • 17444364161 scopus 로고    scopus 로고
    • Divide and conquer algorithms for com puting the eigendecomposition of symmetric diagonal-plus-semiseparable matrices
    • N. MASTRONARDI, E. VAN CAMP, AND M. VAN BAREL, Divide and conquer algorithms for com puting the eigendecomposition of symmetric diagonal-plus-semiseparable matrices, Numer. Algorithms, 39 (2005), pp. 379-398.
    • (2005) Numer. Algorithms , vol.39 , pp. 379-398
    • Mastronardi, N.1    Van Camp, E.2    Van Barel, M.3
  • 12
    • 0034421232 scopus 로고    scopus 로고
    • Relatively robust representations of symmetric tridiagonals
    • B. N. PARLETT AND I. S. DHILLON, Relatively robust representations of symmetric tridiagonals, Linear Algebra Appl., 309 (2000), pp. 121-151.
    • (2000) Linear Algebra Appl. , vol.309 , pp. 121-151
    • Parlett, B.N.1    Dhillon, I.S.2
  • 14
    • 11144311774 scopus 로고    scopus 로고
    • The Interplay of Ranks of Submatrices
    • G. STRANG AND T. NGUYEN, The Interplay of Ranks of Submatrices, SIAM Rev., 46 (2004), pp. 637-646.
    • (2004) SIAM Rev. , vol.46 , pp. 637-646
    • Strang, G.1    Nguyen, T.2
  • 17
    • 1442314109 scopus 로고    scopus 로고
    • Two fast algorithms for solving diagonal-plus- semiseparable linear systems
    • E. VAN CAMP, N. MASTRONARDI, AND M. VAN BAREL, Two fast algorithms for solving diagonal-plus- semiseparable linear systems, J. Comput. Appl. Math., 164-165 (2004), pp. 731-747.
    • (2004) J. Comput. Appl. Math. , vol.164-165 , pp. 731-747
    • Van Camp, E.1    Mastronardi, N.2    Van Barel, M.3
  • 20
    • 0034949475 scopus 로고    scopus 로고
    • Svdman - Singular value decomposition analysis of microarray data
    • M. E. WALL, P.A. DYCK, AND T. S. BRETTIN, Svdman - singular value decomposition analysis of microarray data, Bioinform., 17 (2001), pp. 566-568.
    • (2001) Bioinform. , vol.17 , pp. 566-568
    • Wall, M.E.1    Dyck, P.A.2    Brettin, T.S.3
  • 21
    • 2542430932 scopus 로고    scopus 로고
    • Singular value decomposition and principal component analysis
    • D. P. Berrar, W. Dubitzky, and M. Granzow, eds., Kluwer Academic, Dordrecht, The Netherlands
    • M. E. WALL, A. RECHTSTEINER, AND L. M. ROCHA, Singular value decomposition and principal component analysis, in A Practical Approach to Microarray Data Analysis, D. P. Berrar, W. Dubitzky, and M. Granzow, eds., Kluwer Academic, Dordrecht, The Netherlands, 2003, pp. 91-109.
    • (2003) A Practical Approach to Microarray Data Analysis , pp. 91-109
    • Wall, M.E.1    Rechtsteiner, A.2    Rocha, L.M.3
  • 22
    • 0001118747 scopus 로고    scopus 로고
    • QR-like algorithms: An overview of convergence theory and practice
    • The Mathematics of Numerical Analysis, AMS, Providence, RI
    • D. S. WATKINS, QR-like algorithms: An overview of convergence theory and practice, in The Mathematics of Numerical Analysis, Lectures in Appl. Math. 32, AMS, Providence, RI, 1996, pp. 879-893.
    • (1996) Lectures in Appl. Math. , vol.32 , pp. 879-893
    • Watkins, D.S.1
  • 23
    • 0002732714 scopus 로고
    • Convergence of algorithms of decomposition type for the eigenvalue problem
    • D. S. WATKINS AND L. ELSNER, Convergence of algorithms of decomposition type for the eigenvalue problem, Linear Algebra Appl., 143 (1991), pp. 19-47.
    • (1991) Linear Algebra Appl. , vol.143 , pp. 19-47
    • Watkins, D.S.1    Elsner, L.2
  • 24
    • 0034800371 scopus 로고    scopus 로고
    • Principal component analysis for clustering gene expression data
    • M. K. S. YEUNG AND W. L. RUZZO, Principal component analysis for clustering gene expression data, Bioinform., 17 (2001), pp. 763-774.
    • (2001) Bioinform. , vol.17 , pp. 763-774
    • Yeung, M.K.S.1    Ruzzo, W.L.2
  • 25
    • 0037197936 scopus 로고    scopus 로고
    • Reverse engineering gene networks using singular value decomposition and robust regression
    • M. K. S. YEUNG, J. TEGNéR, AND J. J. COLLINS, EDS.
    • M. K. S. YEUNG, J. TEGNéR, AND J. J. COLLINS, EDS., Reverse engineering gene networks using singular value decomposition and robust regression, Proc. Natl. Acad. Sci., 99 (2002), pp. 6163-6168.
    • (2002) Proc. Natl. Acad. Sci. , vol.99 , pp. 6163-6168


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.