Convergence of the Least Squares Shadowing Method for Computing Derivative of Ergodic Averages
Name
Wang-2014-Convergence of the l.pdf
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1.29 MB
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Adobe PDF
Checksum (MD5)
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Author(s)
Wang, Qiqi
Date Issued
January 2014
Journal
SIAM Journal on Numerical Analysis
Publisher
Society for Industrial and Applied Mathematics
Citation
Wang, Qiqi. “Convergence of the Least Squares Shadowing Method for Computing Derivative of Ergodic Averages.” SIAM Journal on Numerical Analysis 52, no. 1 (January 2014): 156–170. © 2014 Society for Industrial and Applied Mathematics.
Version
Final published version
Abstract
For a parameterized hyperbolic system $u_{i+1} = f(u_i,s)$, the derivative of an ergodic average $\langle J\rangle = \lim_{n\rightarrow\infty} \frac1n \sum_1^n J(u_i,s)$ to the parameter $s$ can be computed via the least squares shadowing method. This method solves a constrained least squares problem and computes an approximation to the desired derivative $\frac{d\langle J\rangle}{ds}$ from the solution. This paper proves that as the size of the least squares problem approaches infinity, the computed approximation converges to the true derivative.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/130917065
