A Bootstrap Method for Sum-of-Poles Approximations
- 382 Downloads
A bootstrap method is presented for finding efficient sum-of-poles approximations of causal functions. The method is based on a recursive application of the nonlinear least squares optimization scheme developed in (Alpert et al. in SIAM J. Numer. Anal. 37:1138–1164, 2000), followed by the balanced truncation method for model reduction in computational control theory as a final optimization step. The method is expected to be useful for a fairly large class of causal functions encountered in engineering and applied physics. The performance of the method and its application to computational physics are illustrated via several numerical examples.
KeywordsRational approximation Sum-of-poles approximation Model reduction Balanced truncation method Square root method
S. Jiang was supported in part by National Science Foundation under grant CCF-0905395 and would like to thank Dr. Bradley Alpert at National Institute of Standards and Technology for many useful discussions on this project. Both authors would like to thank the anonymous referees for their careful reading and very useful suggestions which have greatly enhanced the presentation of the work.
- 1.Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions. Dover, New York (1965) Google Scholar
- 20.Jackson, J.D.: Classical Electrodynamics. Wiley, New York (1998) Google Scholar
- 21.Jiang, S.: Fast evaluation of the nonreflecting boundary conditions for the Schrödinger equation. Ph.D. thesis, Courant Institute of Mathematical Sciences, New York University, New York (2001) Google Scholar