@article{(Open Science Index):https://publications.waset.org/pdf/7202, title = {A Contractor for the Symmetric Solution Set}, author = {Milan Hladik}, country = {}, institution = {}, abstract = {The symmetric solution set Σ sym is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A and A, and b lies between b and b. We present a contractor for Σ sym, which is an iterative method that starts with some initial enclosure of Σ sym (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments. }, journal = {International Journal of Mathematical and Computational Sciences}, volume = {4}, number = {11}, year = {2010}, pages = {1422 - 1427}, ee = {https://publications.waset.org/pdf/7202}, url = {https://publications.waset.org/vol/47}, bibsource = {https://publications.waset.org/}, issn = {eISSN: 1307-6892}, publisher = {World Academy of Science, Engineering and Technology}, index = {Open Science Index 47, 2010}, }