A general algorithm for the direct inversion of data to yield unknown functions entering physical systems is presented. Of particular interest are linear and non-linear dynamical systems. The potential broad applicability of this method is examined in the context of a number of coefficient-recovery problems for partial differential equations. Stability issues are addressed and a stabilization approach, based on inverse asymptotic tracking, is proposed. Numerical examples for a simple illustration are presented, demonstrating the effectiveness of the algorithm.
Copyright © 1994 IOP Publishing. This article first appeared in Inverse Problems 10, no. 5 (1994): 1099-114. doi:10.1088/0266-5611/10/5/007.
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Caudill, Lester F., Herschel Rabitz, and Attila Askar. "A Direct Method for the Inversion of Physical Systems." Inverse Problems 10, no. 5 (1994): 1099-114. doi:10.1088/0266-5611/10/5/007.