The reconstruction of Sturm-Liouville operators

@inproceedings{Rundell1992TheRO,
  title={The reconstruction of Sturm-Liouville operators},
  author={William Rundell and Paul E. Sacks},
  year={1992}
}
The authors give a constructive algorithm for the inverse Sturm-Liouville operator in non-potential form. They emphasize the unknown impedance case, i.e. the recovery of the coefficient a(x) in (a(x)u'(x))'+ lambda a(x)u(x)=0 from spectral data. It is shown that many of the formulations of this problem are equivalent to solving an overdetermined boundary value problem for a certain hyperbolic operator. An iterative procedure for solving this latter problem is developed and numerical examples… CONTINUE READING

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