Abstract
An overdetermined system of complex linear equations is solved in the maximum norm by an iterative algorithm in which each iteration has two phases. Phase 1 concentrates on the combinatorial problem of identifying the active set of equations where the residual magnitude attains the maximum, and Phase 2 concentrates on the numerical problem of accurately solving the equations on the active set. Phase 1 is aimed at building up the set of active equations by means of an interior point method applied to the equivalent real semi-infinite linear program. Phase 2 uses the quadratically convergent Newton method to find the solution to the equality constrained problem on the current active set. A theoretical convergence proof has not been found, but numerical examples show rapid convergence.
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