ABSTRACT
This is the first of four chapters on the solution of underdetermined consistent systems of linear equations subject to certain types of constraints. For consistent underdetermined systems of linear equations, the residual vector is zero. Hence, the constraints are on the solution vector of the system, not on the residual vector. In this chapter, the constraint is that the L1 norm of the solution vector be as small as possible. Consider the underdetermined system of linear equations
Ca = f C = (cij) is a given real n by m matrix of rank k, k ≤ n < m, and f = (fi) is a given real n-vector. It is required to calculate a solution m-vector a = (aj) for this system.
