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The Application of Preconditioned Jacobi-Davidson Methods in Pole-zero Analysis

  • J. Rommes
  • C. W. Bomhof
  • H. A. van der Vorst
  • E. J. W. ter Maten
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 4)

Abstract

The application of Jacobi-Davidson style methods in electric circuit simulation will be discussed in comparison with other iterative methods (Arnoldi) and direct methods (QR, QZ). Numerical results show that the use of a preconditioner to solve the correction equation may improve the Jacobi-Davidson process, but may also cause computational and stability problems when solving the correction equation. Furthermore, some techniques to improve the stability and accuracy of the process will be given.

Keywords

Iterative Method Jordan Block Correction Equation Resp Onse Restart Arnoldi Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    http://www.math.uu.nl/people/sleijpen/JD.software/JDQR.html/people/sleijpen/JD.software/JDQR.html.
  2. 2.
    http://www.math.uu.nl/people/sleijpen/JD.software/JDQZ.html/people/sleijpen/JD.software/JDQZ.html.
  3. 3.
  4. 4.
    Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., and Van Der Vorst, H., Eds. Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide. SIAM, 2000.Google Scholar
  5. 5.
    Bomhof, C. Jacobi-Davidson methods for eigenvalue problems in pole zero analysis. Nat.Lab. Unclassified Report 012/97, Philips Electronics NV, 1997.Google Scholar
  6. 6.
    Bomhof, C. Iterative and parallel methods for linear systems, with applications in circuit simulation. PhD thesis, Utrecht University, 2001.Google Scholar
  7. 7.
    Feldmann, P., and Freund, R. W. Efficient linear circuit analysis by Padé approximation via the Lanczos process. IEEE Trans. CAD14 (1995), 639–649.CrossRefGoogle Scholar
  8. 7.
    Fokkema, D. R., Leijpen, G.L., and Van Der Vorst, H. A. Jacobi-Davidson style QR and QZ algorithms for the reduction of matrix pencils. SIAM J. Sc. Comp. 20, 1 (1998), 94-125.Google Scholar
  9. 9.
    Heres, P. J., and Schilders, W. H. Reduced order modelling of RLC-networks using an SVD-Laguerre based method. In SCEE 2002 Conference Proceedings (2002).Google Scholar
  10. 10.
    Rommes, J. Jacobi-Davidson methods and preconditioning with applications in pole-zero analysis. Master’s thesis, Utrecht University, 2002.Google Scholar
  11. 11.
    Rommes, J., Van Der Vorst, H.A., and Ter Maten, E. J. W. Jacobi-Davidson Methods and Preconditioning with Applications in Pole-zero Analysis. In Progress in Industrial Mathematics at ECMI 2002 2002.Google Scholar
  12. 12.
    Saad, Y. Iterative methods for sparse linear systems. PWS Publishing Company, 1996.Google Scholar
  13. 13.
    Sleijpen, G.L., and VAN DER Vorst H. A. A Jacobi-Davidson Iteration Method for Linear Eigenvalue Problems. SIAM Review 42, 2 (2000), 267–293.MathSciNetCrossRefGoogle Scholar
  14. 14.
    TERMaten, E.J.W. Numerical methods for frequency domain analysis of electronic circuits. Surv. Maths. Ind., 8 (1998), 171–185.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • J. Rommes
    • 1
  • C. W. Bomhof
    • 2
  • H. A. van der Vorst
    • 1
  • E. J. W. ter Maten
    • 3
  1. 1.Utrecht UniversityThe Netherlands
  2. 2.Plaxis BVDelftThe Netherlands
  3. 3.Philips Research LaboratoriesEindhoven University of TechnologyThe Netherlands

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