A bootstrap method for sum-of-poles approximations

Kuan Xu; Shidong Jiang

doi:10.1007/s10915-012-9620-9

A bootstrap method for sum-of-poles approximations

Kuan Xu
, Shidong Jiang

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	16-39
Number of pages	24
Journal	Journal of Scientific Computing
Volume	55
Issue number	1
DOIs	https://doi.org/10.1007/s10915-012-9620-9
State	Published - Apr 2013

All Science Journal Classification (ASJC) codes

Software
Theoretical Computer Science
Numerical Analysis
General Engineering
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

Keywords

Balanced truncation method
Model reduction
Rational approximation
Square root method
Sum-of-poles approximation

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10.1007/s10915-012-9620-9

Cite this

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abstract = "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.",

keywords = "Balanced truncation method, Model reduction, Rational approximation, Square root method, Sum-of-poles approximation",

author = "Kuan Xu and Shidong Jiang",

note = "Funding Information: Acknowledgements 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.",

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N2 - 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.

AB - 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.

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KW - Rational approximation

KW - Square root method

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A bootstrap method for sum-of-poles approximations

Abstract

All Science Journal Classification (ASJC) codes

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