Solution of Systems of Complex Linear Equations in the L Infinity Norm with Constraints on the Unknowns.
Abstract
An algorithm for the numerical solution of general systems of complex linear equations in the L infinity, or Chebyshev, norm is presented. The objective is to find complex values for the unknowns so that the maximum magnitude residual of the system is a minimum. The unknowns are required to satisfy certain general convex constraints. In particular, bounds on the magnitudes of the unknowns are imposed. In the algorithm presented here, this problem is replaced by a linearized problem. The linearized problem is a linear program which is generated in such a way that the relative error between its (exact) solution and the (exact) solution of the original problem can be estimated without knowing a priori the solution of either. Furthermore, the maximum relative error can easily be made as small as desired by selecting an appropriate linearized problem. Order of magnitude improvements in both computation time and computer storage requirements in an implementaiton of the simplex algorithm to this linear program are presented. Three numerical examples are included, one of which is a discretized complex function approximation problem. Extrapolation and an active set method are suggested for solving the general problem when greater accuracy is required than can be obtained economically by solving the linearized problems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 18, 1983
- Accession Number
- ADA127883
Entities
People
- Roy L. Streit
Organizations
- Naval Underwater Systems Center