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Volumn 67, Issue 221, 1998, Pages 271-286

Analysis of third-order methods for secular equations

Author keywords

Nonlinear approximation; Secular equation; Third order convergence

Indexed keywords


EID: 0032341231     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-98-00884-9     Document Type: Article
Times cited : (12)

References (25)
  • 1
    • 0039923684 scopus 로고
    • A parallel divide and conquer algorithm for the generalized real symmetric definite tridiagonal eigenproblem
    • L. Reichel, A. Ruttan and R.S. Varga, eds., de Gruyter, Berlin. MR 94k:65051
    • Borges, C.F., Gragg, W.B. (1993): A parallel divide and conquer algorithm for the generalized real symmetric definite tridiagonal eigenproblem. In Numerical Linear Algebra and Scientific Computing, L. Reichel, A. Ruttan and R.S. Varga, eds., pp. 10-28, de Gruyter, Berlin. MR 94k:65051
    • (1993) Numerical Linear Algebra and Scientific Computing , pp. 10-28
    • Borges, C.F.1    Gragg, W.B.2
  • 2
    • 0013201091 scopus 로고
    • On Halley's variation of Newton's method
    • MR 57:1866
    • Brown G.H., Jr. (1978): On Halley's variation of Newton's method. Amer. Math. Monthly 84, pp. 726-728. MR 57:1866
    • (1978) Amer. Math. Monthly , vol.84 , pp. 726-728
    • Brown, G.H.1
  • 3
    • 0002316189 scopus 로고
    • Rank-one modification of the symmetric eigenproblem
    • MR 80g:65038
    • Bunch, J.R., Nielsen, C.P., Sorensen, D.C. (1978): Rank-one modification of the symmetric eigenproblem. Numer. Math. 31, pp. 31-48. MR 80g:65038
    • (1978) Numer. Math. , vol.31 , pp. 31-48
    • Bunch, J.R.1    Nielsen, C.P.2    Sorensen, D.C.3
  • 4
    • 34250270918 scopus 로고
    • Updating the singular value decomposition
    • MR 80m:65025
    • Bunch, J.R., Nielsen, C.P. (1978): Updating the singular value decomposition. Numer. Math. 31, pp. 111-129. MR 80m:65025
    • (1978) Numer. Math. , vol.31 , pp. 111-129
    • Bunch, J.R.1    Nielsen, C.P.2
  • 5
    • 0000659575 scopus 로고
    • A divide and conquer method for the symmetric tridiagonal eigenvalue problem
    • MR 82d:65038
    • Cuppen, J.J.M. (1981): A divide and conquer method for the symmetric tridiagonal eigenvalue problem. Numer. Math. 36, pp. 177-195. MR 82d:65038
    • (1981) Numer. Math. , vol.36 , pp. 177-195
    • Cuppen, J.J.M.1
  • 6
    • 0000417182 scopus 로고
    • A fully parallel algorithm for the symmetric eigenvalue problem
    • MR 88f:65054
    • Dongarra, J.J., Sorensen, D.C. (1987): A fully parallel algorithm for the symmetric eigenvalue problem. SIAM J. Sci. Stat. Comput. 8, No.2, pp. s139-s154. MR 88f:65054
    • (1987) SIAM J. Sci. Stat. Comput. , vol.8 , Issue.2
    • Dongarra, J.J.1    Sorensen, D.C.2
  • 8
    • 0000288741 scopus 로고
    • An algorithm for subspace computation with applications in signal processing
    • MR 89f:65040
    • Fuhrmann, D.R. (1988): An algorithm for subspace computation with applications in signal processing. SIAM J. Matrix Anal. Appl. 9, No.2, pp. 213-220. MR 89f:65040
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , Issue.2 , pp. 213-220
    • Fuhrmann, D.R.1
  • 9
    • 38249023522 scopus 로고
    • A constrained eigenvalue problem
    • MR 90e:15008
    • Gander, W., Golub, G.H., von Matt, U. (1989): A constrained eigenvalue problem. Linear Algebra Appl. 114-115, pp. 815-839. MR 90e:15008
    • (1989) Linear Algebra Appl. , vol.114-115 , pp. 815-839
    • Gander, W.1    Golub, G.H.2    Von Matt, U.3
  • 10
    • 0013135929 scopus 로고
    • 2) method for computing the eigensystem of N x N symmetric tridiagonal matrices by the divide and conquer approach
    • MR 91d:65058
    • 2) method for computing the eigensystem of N x N symmetric tridiagonal matrices by the divide and conquer approach. SIAM J. Sci. Stat. Comput. 11, No. 1, pp. 161-173. MR 91d:65058
    • (1990) SIAM J. Sci. Stat. Comput. , vol.11 , Issue.1 , pp. 161-173
    • Gill, D.1    Tadmor, E.2
  • 11
    • 0001070999 scopus 로고
    • Some modified matrix eigenvalue problems
    • MR 48:7569
    • Golub, G.H. (1973): Some modified matrix eigenvalue problems. SIAM Rev. 15, No.2, pp. 318-334. MR 48:7569
    • (1973) SIAM Rev. , vol.15 , Issue.2 , pp. 318-334
    • Golub, G.H.1
  • 12
    • 0000429893 scopus 로고
    • A divide and conquer method for unitary and orthogonal eigenproblems
    • MR 91h:65052
    • Gragg, W.B., Reichel, L. (1990): A divide and conquer method for unitary and orthogonal eigenproblems. Numer. Math. 57, pp. 695-718. MR 91h:65052
    • (1990) Numer. Math. , vol.57 , pp. 695-718
    • Gragg, W.B.1    Reichel, L.2
  • 13
    • 0040969900 scopus 로고
    • Parallel divide and conquer algorithms for the symmetric tridiagonal eigenproblem and the bidiagonal singular value problem
    • W.G. Vogt and M.H. Mickle, eds., University of Pittsburgh School of Engineering, Pittsburgh, PA
    • Gragg, W.B., Thornton, J.R., Warner, D.D. (1992): Parallel divide and conquer algorithms for the symmetric tridiagonal eigenproblem and the bidiagonal singular value problem. In Modeling and Simulation, W.G. Vogt and M.H. Mickle, eds., vol. 3, part 1, pp. 49-56. University of Pittsburgh School of Engineering, Pittsburgh, PA.
    • (1992) Modeling and Simulation , vol.3 , Issue.1 PART , pp. 49-56
    • Gragg, W.B.1    Thornton, J.R.2    Warner, D.D.3
  • 14
    • 21844525426 scopus 로고
    • A stable and efficient algorithm for the rank-one modification of the symmetric eigenproblem
    • MR 96c:65057
    • Gu M., Eisenstat S.C. (1994): A stable and efficient algorithm for the rank-one modification of the symmetric eigenproblem. SIAM J. Matrix Anal. Appl. 15, No.4, pp. 1266-1276. MR 96c:65057
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , Issue.4 , pp. 1266-1276
    • Gu, M.1    Eisenstat, S.C.2
  • 16
    • 0013137925 scopus 로고
    • Technical Report UCB//CSD-94-851, Computer Science Division, University of California, Berkeley, CA. Also : LAPACK Working Notes 89
    • Li, R.C. (1994): Solving secular equations stably and efficiently. Technical Report UCB//CSD-94-851, Computer Science Division, University of California, Berkeley, CA. Also : LAPACK Working Notes 89.
    • (1994) Solving Secular Equations Stably and Efficiently
    • Li, R.C.1
  • 17
    • 84879517390 scopus 로고
    • Numerical solution of a secular equation
    • MR 95j:65050
    • Melman, A. (1995): Numerical solution of a secular equation. Numer. Math. 69, pp. 483-493. MR 95j:65050
    • (1995) Numer. Math. , vol.69 , pp. 483-493
    • Melman, A.1
  • 18
    • 0031540780 scopus 로고    scopus 로고
    • A unifying convergence analysis of second-order methods for secular equations
    • (1997), CMP 97:02
    • Melman, A. (1997): A unifying convergence analysis of second-order methods for secular equations. Math. Comp. 66 (1997), 333-344. CMP 97:02
    • (1997) Math. Comp. , vol.66 , pp. 333-344
    • Melman, A.1
  • 20
    • 0039191040 scopus 로고
    • On the convergence of the process of tangent hyperbolas
    • (in Russian). MR 14:91f
    • Salehov G.S. (1952): On the convergence of the process of tangent hyperbolas. Dokl. Akad. Nauk SSSR 82, pp. 525-528 (in Russian). MR 14:91f
    • (1952) Dokl. Akad. Nauk SSSR , vol.82 , pp. 525-528
    • Salehov, G.S.1
  • 21
    • 4243339623 scopus 로고
    • The method of tangent hyperbolas
    • (in Russian)
    • Šafiev R.A. (1963): The method of tangent hyperbolas. Dokl. Akad. Nauk SSSR 149, pp. 788-791 (in Russian).
    • (1963) Dokl. Akad. Nauk SSSR , vol.149 , pp. 788-791
    • Šafiev, R.A.1
  • 22
    • 85033873456 scopus 로고    scopus 로고
    • MR 28:734
    • Šafiev R.A. (1963): The method of tangent hyperbolas. Dokl. Akad. Nauk SSSR 149, pp. 788-791 (in Russian). Translation in Soviet Math. Dokl. 4, pp. 482-485. MR 28:734
    • Soviet Math. Dokl. , vol.4 , pp. 482-485
  • 23
    • 14944351893 scopus 로고
    • On the geometry of Halley's method
    • MR 96f:01019
    • Scavo T.R. and Thoo J.B. (1995): On the geometry of Halley's method. Amer. Math. Monthly 102, pp. 417-426. MR 96f:01019
    • (1995) Amer. Math. Monthly , vol.102 , pp. 417-426
    • Scavo, T.R.1    Thoo, J.B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.