In this paper, we present an implementation of a fast multiscale collocation method for boundary integral equations of the second kind, and its application to solving an inverse boundary value problem of recovering a coefficient function from a boundary measurement. We illustrate by numerical examples the insensitive nature of the map from the coefficient to measurement, and design and test a Gauss–Newton iteration algorithm for obtaining the best estimate of the unknown coefficient from the given measurement based on a least-squares formulation. Copyright © 2004 John Wiley & Sons, Ltd.