Geodesic
Dynamical inverse problem for nonselfadjoint Sturm--Liouville operator
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 27, Tome 250 (1998), pp. 7-21

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The paper deals with an approach to the Inverse Problem based upon their relations to the Boundary Control Theory (so-called the BC-method). A procedure of recovering a nonsymmetric matrix-function (potential) given on a semiaxis via the dynamical response operator is described. The results of numerical testing are demonstrated. 
@article{ZNSL_1998_250_a0,
     author = {S. A. Avdonin and M. I. Belishev and Yu. S. Rozhkov},
     title = {Dynamical inverse problem for nonselfadjoint {Sturm--Liouville} operator},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {7--21},
     publisher = {mathdoc},
     volume = {250},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_250_a0/}
}
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S. A. Avdonin; M. I. Belishev; Yu. S. Rozhkov. Dynamical inverse problem for nonselfadjoint Sturm--Liouville operator. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 27, Tome 250 (1998), pp. 7-21. http://geodesic.mathdoc.fr/item/ZNSL_1998_250_a0/