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The collage coding method and its application to an inverse problem for the Lorenz system. (English) Zbl 1114.65086

Summary: A Lorenz system inverse problem featuring noisy partial data sets is considered via the method of collage coding. Collage coding is a rigorously-established approach to such problems, with its roots in fractal imaging, and its theoretical basis being Banach’s fixed point theorem and some recent related results. For comparison purposes, results for this inverse problem obtained by using other methods are mentioned. A framework for treating general inverse problems involving partial data sets in a similar way is also outlined.

MSC:

65L09 Numerical solution of inverse problems involving ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34A55 Inverse problems involving ordinary differential equations
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