  We consider the problem of finding sparse solutions to a system of
underdetermined nonlinear system of equations. The methods are based on a
Gauss-Newton approach with line search where the search direction is found by
solving a linearized problem using only a subset of the columns in the
Jacobian. The choice of columns in the Jacobian is made through a greedy
approach looking at either maximum descent or an approach corresponding to
orthogonal matching for linear problems. The methods are shown to be convergent
and efficient and outperform the $\ell_1$ approach on the test problems
presented.
