@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},
	}