  We describe the volume dependence of matrix elements of local boundary fields
to all orders in inverse powers of the volume. Using the scaling boundary
Lee-Yang model as testing ground, we compare the matrix elements extracted from
boundary truncated conformal space approach to exact form factors obtained
using the bootstrap method. We obtain solid confirmation for the boundary form
factor bootstrap, which is different from all previously available tests in
that it is a non-perturbative and direct comparison of exact form factors to
multi-particle matrix elements of local operators, computed from the
Hamiltonian formulation of the quantum field theory.
