For the Sturm-Liouville operator L =L,: .VP+ -p” +pv one seeks to reconstruct the coefficient p from knowledge of the sequence of eigen-frequencies (Aj with LJ? =Ajn for some y j # 0). An implementable scheme is: for some N determine pnr so (approximately) pN has minimum norm with eigen-frequencies { A , . . . . .IN/ as given. This is the method ot’ ’generalised interpolation‘ and is shown to g...