  An effective algorithm is presented for solving the Beltrami equation df/dz =
mu (df/dzbar) in a planar disk. The disk is triangulated in a simple way and f
is approximated by piecewise linear mappings; the images of the vertices of the
triangles are defined by an overdetermined system of linear equations. (Certain
apparently nonlinear conditions on the boundary are eliminated by means of a
symmetry construction.) The linear system is sparse and its solution is
obtained by standard least-squares, so the algorithm involves no evaluation of
singular integrals nor any iterative procedure for obtaining a single
approximation of f. Numerical examples are provided, including a deformation in
a Teichm\"uller space of a Fuchsian group.
