Inverse problems for ODEs using contraction maps and suboptimality of the ‘collage method’

@article{Kunze2004InversePF,
  title={Inverse problems for ODEs using contraction maps and suboptimality of the ‘collage method’},
  author={H E Kunze and J E Hicken and E R Vrscay},
  journal={Inverse Problems},
  year={2004},
  volume={20},
  pages={977 - 991}
}
Broad classes of inverse problems in differential and integral equations can be cast in the following framework: the optimal approximation of a target x of a suitable metric space X by the fixed point of a contraction map T on X. The ‘collage method’ attempts to solve such inverse problems by finding an operator Tc that maps the target x as close as possible to itself. In the case of ODEs, the appropriate contraction maps are integral Picard operators. In practice, the target solutions possibly…