CALCULATION OF DISCRETE LINEAR MAXIMUM NORM APPROXIMATIONS

Direct methods for the solution of linear approximation problems tend to fail in practice because of numerical instabilities. Difficulties arise from an undesired accumulation of round-off errors. In [3] and in chapter 2 of this paper effective and inexpensive tests are developed to recognize numerical difficulties and stabilize numerical methods by iterative refinement and restart procedures, if necessary. On the ground of this, a stabilized version of a modified revised dual simplex algorithm can be developed capable of solving the approximation problems under consideration. The technical details of this method and a FORTRAN implementation are given in [4]. Numerical examples are discussed to illustrate that the developed method is superior to commonly used algorithms not only by a broader range of applications and more stability, but also by considerably less storage requirement (for large problems), while the execution times are comparable or less. © 1978 Springer-Verlag.