**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31014

##### A Contractor for the Symmetric Solution Set

**Authors:**
Milan Hladik

**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.

**Keywords:**
Linear interval systems,
solution set,
interval matrix,
symmetric matrix

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1333366

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