메뉴 건너뛰기




Volumn 1, Issue 4, 2002, Pages 269-282

Solving Symmetric Arrowhead and Special Tridiagonal Linear Systems by Fast Approximate Inverse Preconditioning

Author keywords

approximate factorization; approximate inverses; arrowhead matrix; bordered diagonal matrix; parallel iterative methods; preconditioning; special tridiagonal systems

Indexed keywords


EID: 33645433929     PISSN: 15701166     EISSN: 15729214     Source Type: Journal    
DOI: 10.1023/A:1021630031889     Document Type: Article
Times cited : (12)

References (19)
  • 1
    • 0039715485 scopus 로고
    • QR-like algorithms for symmetric arrow matrices
    • Arbenz, P. and Golub, G.: QR-like algorithms for symmetric arrow matrices, SIAM J. Matrix Anal. Appl. 13 (1992), 655-658.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 655-658
    • Arbenz, P.1    Golub, G.2
  • 2
    • 84966211417 scopus 로고
    • On Fourier-Toeplitz methods for separable elliptic problems
    • Fisher, D., Golub, G., Hald, O., Leiva, C. and Widlund, O.: On Fourier-Toeplitz methods for separable elliptic problems, Math. Comp. 28 (1974), 349-368.
    • (1974) Math. Comp , vol.28 , pp. 349-368
    • Fisher, D.1    Golub, G.2    Hald, O.3    Leiva, C.4    Widlund, O.5
  • 3
    • 0001070999 scopus 로고
    • Some modified matrix eigenvalue problems
    • Golub, G.: Some modified matrix eigenvalue problems, SIAM Rev. 15 (1973), 318-334.
    • (1973) SIAM Rev. , vol.15 , pp. 318-334
    • Golub, G.1
  • 4
    • 0001190030 scopus 로고
    • The numerically stable reconstruction of Jacobi matrix from spectral data
    • Gragg, B. and Harrod W.: The numerically stable reconstruction of Jacobi matrix from spectral data, Numer. Math. 44 (1984), 317-355.
    • (1984) Numer. Math. , vol.44 , pp. 317-355
    • Gragg, B.1    Harrod, W.2
  • 5
    • 84888592232 scopus 로고    scopus 로고
    • A fast explicit preconditioned symmetric finite element scheme
    • Gravvanis, G. A.: A fast explicit preconditioned symmetric finite element scheme, Neural Parallel Sci. Comput. 9(1) (2001), 59-66.
    • (2001) Neural Parallel Sci. Comput. , vol.9 , Issue.1 , pp. 59-66
    • Gravvanis, G.A.1
  • 6
    • 0013189223 scopus 로고    scopus 로고
    • Fast explicit approximate inverses for solving linear and non-linear finite difference equations
    • Gravvanis, G. A.: Fast explicit approximate inverses for solving linear and non-linear finite difference equations, Internat. J. Differential Equations Appl. 1(4) (2000), 451-473.
    • (2000) Internat. J. Differential Equations Appl. , vol.1 , Issue.4 , pp. 451-473
    • Gravvanis, G.A.1
  • 7
    • 0013251505 scopus 로고    scopus 로고
    • Generalized approximate inverse preconditioning for solving non-linear elliptic boundary-value problems
    • Gravvanis, G. A.: Generalized approximate inverse preconditioning for solving non-linear elliptic boundary-value problems, Internat. J. Appl. Math. 2(11) (2000), 1363-1378.
    • (2000) Internat. J. Appl. Math. , vol.2 , Issue.11 , pp. 1363-1378
    • Gravvanis, G.A.1
  • 9
    • 0032625710 scopus 로고    scopus 로고
    • Approximate inverse banded matrix techniques
    • Gravvanis, G. A.: Approximate inverse banded matrix techniques, Engrg. Comput. 16(3) (1999), 337-346.
    • (1999) Engrg. Comput. , vol.16 , Issue.3 , pp. 337-346
    • Gravvanis, G.A.1
  • 10
    • 0029777947 scopus 로고    scopus 로고
    • The rate of convergence of explicit approximate inverse preconditioning
    • Gravvanis, G. A.: The rate of convergence of explicit approximate inverse preconditioning, Internat. J. Comput. Math. 60 (1996), 77-89.
    • (1996) Internat. J. Comput. Math. , vol.60 , pp. 77-89
    • Gravvanis, G.A.1
  • 11
    • 0029541853 scopus 로고
    • Explicit preconditioned methods for solving 3D boundary value problems by approximate inverse finite element matrix techniques
    • Gravvanis, G. A.: Explicit preconditioned methods for solving 3D boundary value problems by approximate inverse finite element matrix techniques, Internat. J. Comput. Math. 56 (1995), 77-93.
    • (1995) Internat. J. Comput. Math. , vol.56 , pp. 77-93
    • Gravvanis, G.A.1
  • 12
    • 0028495951 scopus 로고
    • A three dimensional symmetric linear equation solver
    • Gravvanis, G. A.: A three dimensional symmetric linear equation solver, Comm. Numer. Methods Engrg. 10(9) (1994), 717-730.
    • (1994) Comm. Numer. Methods Engrg. , vol.10 , Issue.9 , pp. 717-730
    • Gravvanis, G.A.1
  • 13
    • 0013255656 scopus 로고
    • Numerical solution of non-linear elliptic boundary-value problems by isomorphic iterative methods
    • Lipitakis, E. A. and Evans, D. J.: Numerical solution of non-linear elliptic boundary-value problems by isomorphic iterative methods, Interact. J. Comput. Math. 20 (1986), 261-282.
    • (1986) Interact. J. Comput. Math. , vol.20 , pp. 261-282
    • Lipitakis, E.A.1    Evans, D.J.2
  • 14
    • 38249017274 scopus 로고
    • Computing the eigenproblem and eigenvectors of arrowhead matrices
    • O'Leary, D. and Stewart, G.: Computing the eigenproblem and eigenvectors of arrowhead matrices, J. Comput. Phys. 90 (1990), 497-505.
    • (1990) J. Comput. Phys. , vol.90 , pp. 497-505
    • O'Leary, D.1    Stewart, G.2
  • 16
    • 0009345450 scopus 로고
    • The use of refined error bound when updating eigenvalues of tridiagonals
    • Parlett, B. and Nour-Omid, B.: The use of refined error bound when updating eigenvalues of tridiagonals, Linear Algebra Appl. 68 (1985), 179-219.
    • (1985) Linear Algebra Appl. , vol.68 , pp. 179-219
    • Parlett, B.1    Nour-Omid, B.2
  • 17
    • 0039715520 scopus 로고
    • On Jacobi rotation patterns, In: Experimental Arithmetic, High Speed Computing and Mathematics
    • Rutishauser, H.: On Jacobi rotation patterns, In: Experimental Arithmetic, High Speed Computing and Mathematics, Proc. Sympos. Appl. Math. 15, Amer. Math. Soc., Providence, 1963, pp. 219-239.
    • (1963) Proc. Sympos. Appl. Math. 15, Amer. Math. Soc., Providence , pp. 219-239
    • Rutishauser, H.1
  • 18
    • 0039123306 scopus 로고
    • A two-way chasing scheme for reducing a symmetric arrowhead matrix to tridiagonal form
    • Zha, H.: A two-way chasing scheme for reducing a symmetric arrowhead matrix to tridiagonal form, J. Numer. Algebra Appl. 1 (1992), 49-57.
    • (1992) J. Numer. Algebra Appl. , vol.1 , pp. 49-57
    • Zha, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.