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|a Wang, Qiqi
|e author
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|a Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
|e contributor
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|a Wang, Qiqi
|e contributor
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|a Convergence of the Least Squares Shadowing Method for Computing Derivative of Ergodic Averages
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|b Society for Industrial and Applied Mathematics,
|c 2014-07-01T19:48:22Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/88173
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|a 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.
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|a United States. Air Force Office of Scientific Research (STTR contract FA9550-12-C-0065)
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|a United States. National Aeronautics and Space Administration
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|a en_US
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|a Article
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|t SIAM Journal on Numerical Analysis
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