**** Update: this paper will appear in the Journal of the European Mathematical Society ****

Jonathan Ben-Artzi, Marco Marletta and Frank Rösler submitted the paper *Computing Scattering Resonances* in which they ask the question:

Does there exist a universal algorithm for computing the resonances of Schrödinger operators with complex potentials?

Resonances are special modes that are *nearly* eigenvalues, in the sense that corresponding to them there are states that do not belong to the functional space (typically because they are not sufficiently localized). More precisely, let be a Schrödinger operator with compactly supported and let be a smooth cutoff function that is identically 1 on the support of . Then

Definition (resonance).A resonance of is defined to be a pole of the meromorphic operator-valued function .

This paper provides an affirmative answer to the above question. The only *a priori* information required is the size of the support of . With this knowledge at hand, this paper provides an algorithm (which is also implemented numerically) which only needs to read finitely many pointwise evaluations . These values are used to construct a approximation of which is shown to converge in an appropriate sense as more and more values of are sampled.