论文信息 - The application of preconditioned Jacobi-Davidson methods in pole-zero analysis

The application of preconditioned Jacobi-Davidson methods in pole-zero analysis

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.

van der Henk Vorst | ter Ejw Jan Maten | Joost Rommes | CW Bomhof

[1] Joost Rommes,et al. Jacobi-Davidson Methods and Preconditioning with Applications in Pole-zero Analysis , 2004 .

[2] H. K. Lee,et al. Numerical Solution of the Stationary Navier-Stokes Equations Using a Multilevel Finite Element Method , 1998, SIAM J. Sci. Comput..

[3] Gerard L. G. Sleijpen,et al. Jacobi-Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils , 1998, SIAM J. Sci. Comput..

[4] Roland W. Freund,et al. Efficient linear circuit analysis by Pade´ approximation via the Lanczos process , 1994, EURO-DAC '94.

[5] Wha Wil Schilders,et al. Reduced Order Modelling of RLC-networks Using an SVD-Laguerre Based Method , 2004 .

[6] Yousef Saad,et al. Iterative methods for sparse linear systems , 2003 .

[7] Gerard L. G. Sleijpen,et al. A Jacobi-Davidson Iteration Method for Linear Eigenvalue Problems , 1996, SIAM J. Matrix Anal. Appl..

[8] Jack Dongarra,et al. Templates for the Solution of Algebraic Eigenvalue Problems , 2000, Software, environments, tools.

[9] C. Bomhof. Iterative and parallel methods for linear systems, with applications in circuit simulation , 2001 .