메뉴 건너뛰기




Volumn 10, Issue 4, 2003, Pages 357-375

Algebraic formulations for the solution of the nullspace-free eigenvalue problem using the inexact Shift-and-Invert Lanczos method

Author keywords

Generalized eigenvalue problem; Iterative system solvers; Shift and Invert Lanczos

Indexed keywords


EID: 0037839914     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.307     Document Type: Article
Times cited : (14)

References (29)
  • 2
    • 0000807589 scopus 로고    scopus 로고
    • Computational models of electromagnetic resonators: Analysis of edge element approximation
    • Boffi D, Fernandes P, Gastaldi L, Perugia I. Computational models of electromagnetic resonators: analysis of edge element approximation. SIAM Journal of Numerical Analysis 1999; 36:1264-1290.
    • (1999) SIAM Journal of Numerical Analysis , vol.36 , pp. 1264-1290
    • Boffi, D.1    Fernandes, P.2    Gastaldi, L.3    Perugia, I.4
  • 3
    • 0037739571 scopus 로고    scopus 로고
    • Multilevel method for mixed eigenproblems
    • Universität Tübingen
    • Hiptmair R, Neymeyr K. Multilevel method for mixed eigenproblems. Technical Report No. 159, Universität Tübingen, 2001.
    • (2001) Technical Report No. 159 , vol.159
    • Hiptmair, R.1    Neymeyr, K.2
  • 7
    • 45949114901 scopus 로고
    • Mixed and penalty formulations for finite element analysis of an eigenvalue problem in electromagnetism
    • Kikuchi F. Mixed and penalty formulations for finite element analysis of an eigenvalue problem in electromagnetism. Computer Methods in Applied Mechanics and Engineering 1987; 64:509-521.
    • (1987) Computer Methods in Applied Mechanics and Engineering , vol.64 , pp. 509-521
    • Kikuchi, F.1
  • 9
    • 0001976163 scopus 로고
    • A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems
    • Grimes R, Lewis J, Simon H. A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems. SIAM Journal of Matrix Analysis and Applications 1994; 15:228-272.
    • (1994) SIAM Journal of Matrix Analysis and Applications , vol.15 , pp. 228-272
    • Grimes, R.1    Lewis, J.2    Simon, H.3
  • 10
    • 0039500754 scopus 로고    scopus 로고
    • Implicitly restarted Arnoldi with purification for the Shift-Invert transformation
    • Meerbergen K, Spence A. Implicitly restarted Arnoldi with purification for the Shift-Invert transformation. Mathematics of Computation 1997; 66:667-689.
    • (1997) Mathematics of Computation , vol.66 , pp. 667-689
    • Meerbergen, K.1    Spence, A.2
  • 11
    • 0033472157 scopus 로고    scopus 로고
    • A comparison of solvers for large eigenvalue problems occurring in the design of resonant cavities
    • Arbenz P, Geus R. A comparison of solvers for large eigenvalue problems occurring in the design of resonant cavities. Numerical Linear Algebra with Applications 1999; 6:3-16.
    • (1999) Numerical Linear Algebra with Applications , vol.6 , pp. 3-16
    • Arbenz, P.1    Geus, R.2
  • 12
    • 0142032918 scopus 로고    scopus 로고
    • On positive semidefinite matrices with known null space
    • ETH Zurich, Computer Science Department
    • Arbenz P, Drmac Z. On positive semidefinite matrices with known null space. ETH Zurich, Computer Science Department, Technical Report No. 352, 2000.
    • (2000) Technical Report No. 352 , vol.352
    • Arbenz, P.1    Drmac, Z.2
  • 14
    • 0034398887 scopus 로고    scopus 로고
    • Large sparse symmetric eigenvalue problems with homogeneous linear constraints: The Lanczos process with inner-outer iterations
    • Golub G, Zhang Z, Zha H. Large sparse symmetric eigenvalue problems with homogeneous linear constraints: the Lanczos process with inner-outer iterations. Linear Algebra and Applications 2000; 309:289-306.
    • (2000) Linear Algebra and Applications , vol.309 , pp. 289-306
    • Golub, G.1    Zhang, Z.2    Zha, H.3
  • 15
    • 0041730764 scopus 로고    scopus 로고
    • Inexact inverse iterations for the generalized eigenvalue problems
    • Golub GH, Ye Q. Inexact inverse iterations for the generalized eigenvalue problems. BIT 2000; 40:671-684.
    • (2000) BIT , vol.40 , pp. 671-684
    • Golub, G.H.1    Ye, Q.2
  • 16
    • 0009924727 scopus 로고    scopus 로고
    • Inexact Rayleigh quotient-type methods for eigenvalue computations
    • Simoncini V, Eldèn L. Inexact Rayleigh quotient-type methods for eigenvalue computations. BIT 2002; 42(1):159-182.
    • (2002) BIT , vol.42 , Issue.1 , pp. 159-182
    • Simoncini, V.1    Eldèn, L.2
  • 18
    • 0033479131 scopus 로고    scopus 로고
    • The effects of inexact solvers in algorithms for symmetric eigenvalue problems
    • Smit P, Paardekooper M. The effects of inexact solvers in algorithms for symmetric eigenvalue problems. Linear Algebra and Applications 1999; 287:337-357.
    • (1999) Linear Algebra and Applications , vol.287 , pp. 337-357
    • Smit, P.1    Paardekooper, M.2
  • 22
    • 4243465852 scopus 로고    scopus 로고
    • Krylov subspace methods for saddle point problems with indefinite preconditioning
    • IAN-CNR Technical Report No. 1181, to appear
    • Rozložník M, Simoncini V. Krylov subspace methods for saddle point problems with indefinite preconditioning. IAN-CNR Technical Report No. 1181, 2000, SIAM Journal on Matrix Analysis and Applications, to appear.
    • (2000) SIAM Journal on Matrix Analysis and Applications
    • Rozložník, M.1    Simoncini, V.2
  • 23
    • 84985316667 scopus 로고
    • On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling
    • Freund R, Hochbruck M. On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling. Numerical Linear Algebra with Applications 1994; 1:403-420.
    • (1994) Numerical Linear Algebra with Applications , vol.1 , pp. 403-420
    • Freund, R.1    Hochbruck, M.2
  • 24
    • 0001578044 scopus 로고
    • Incomplete factorizations of singular linear systems
    • Notay Y. Incomplete factorizations of singular linear systems. BIT 1989; 29:682-702.
    • (1989) BIT , vol.29 , pp. 682-702
    • Notay, Y.1
  • 25
    • 0000293926 scopus 로고
    • Solving positive (semi)definite linear systems by preconditioned iterative methods
    • Axelsson O, Kolotilina L (eds). Lectures Notes in Mathematics, Springer-Verlag: Berlin
    • Notay Y. Solving positive (semi)definite linear systems by preconditioned iterative methods. In Preconditioned Conjugate Gradient Methods. Axelsson O, Kolotilina L (eds). Lectures Notes in Mathematics, vol. 1457, Springer-Verlag: Berlin, 1990, 105-125.
    • (1990) Preconditioned Conjugate Gradient Methods , vol.1457 , pp. 105-125
    • Notay, Y.1
  • 26
    • 0000893691 scopus 로고    scopus 로고
    • Iterative methods for problems in computational fluid dynamics
    • Chan CT, Golub G (eds). Springer-Verlag: Berlin
    • Elman HC, Silvester DJ, Wathen AJ. Iterative methods for problems in computational fluid dynamics. In Iterative Methods in Scientific Computing, Chan CT, Golub G (eds). Springer-Verlag: Berlin, 1997.
    • (1997) Iterative Methods in Scientific Computing
    • Elman, H.C.1    Silvester, D.J.2    Wathen, A.J.3
  • 27
    • 0034368563 scopus 로고    scopus 로고
    • Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations
    • Perugia I, Simoncini V. Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations. Numerical Linear Algebra with Applications 2000; 7:585-616.
    • (2000) Numerical Linear Algebra with Applications , vol.7 , pp. 585-616
    • Perugia, I.1    Simoncini, V.2
  • 28
    • 0028517184 scopus 로고
    • Fast iterative solution of stabilized Stokes systems part II: Using general block preconditioners
    • Silvester D, Wathen A. Fast iterative solution of stabilized Stokes systems part II: using general block preconditioners. SIAM Journal of Numerical Analysis 1994; 31:1352-1367.
    • (1994) SIAM Journal of Numerical Analysis , vol.31 , pp. 1352-1367
    • Silvester, D.1    Wathen, A.2
  • 29
    • 0141638140 scopus 로고    scopus 로고
    • Techniques for solving general KKT systems
    • SCCM Program, Stanford University
    • Golub G, Greif C. Techniques for solving general KKT systems. Technical Report No. 05, SCCM Program, Stanford University, 2000.
    • (2000) Technical Report No. 05 , vol.5
    • Golub, G.1    Greif, C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.