Computing and Visualizing Solution Sets of Interval Linear Systems

Abstract

The computation of the exact solution set of an interval linear system is a nontrivial task [2, 13]. Even in two and three dimensions a lot of work has to be done. We demonstrate two different realizations. The first approach (see [16]) is based on Java, Java3D, and the BigRational package [21]. An applet allows modifications of the matrix coefficients and/or the coefficients of the right hand side with concurrent real time visualization of the corresponding solution sets. The second approach (see [5]) uses Maple and intpakX [22, 8, 12] to implement routines for the computation and visualization of two and three dimensional solution sets. The regularity of the interval matrix A is verified by showing that ρ(|I-mid^(-1)(A)*Aj|) < 1 [14]. Here, I means the identity matrix, mid(A) denotes the midpoint matrix and ρ denotes the spectral radius of a real matrix.