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This paper develops a variant of the Least Squares Shadowing (LSS) method,which has successfully computed the derivative for several chaotic ODEs andPDEs. The development in this paper aims to simplify Least Squares Shadowingmethod by improving how time dilation is treated. Instead of adding an explicittime dilation term as in the original method, the new variant uses windowing,which can be simpler to implement, especially for PDEs.

Simplified Least Squares Shadowing sensitivity analysis for chaotic ODEs and PDEs