A least distance algorithm for a smooth strictly convex norm

Abstract

An algorithm for approximating a non negative solution of inconsistent systems of linear equations is presented. We define a best approximate solution of a system Ax = b x≥0 to be the vector x≥0 which minimizes the norm of the residual r(x) = b − Ax, for a smooth and strictly convex norm. The algorithm is shown to be feasible and globally convergent. The special case of the ℓ ^p norm is included. In particular, the method converges for 1 < p < 2. A generalization of this algorithm is also given. Numerical results are included.

Keywords:

• Inconsistent system
• smooth strictly convex
• convex norm
• residual norm

C.R. Category:

• G1.3