Computing and Visualizing Solution Sets of Interval Linear Systems

Walter Kr\"amer

University of Wuppertal
42119 Wuppertal, Germany

The computation of the exact solution set of an interval linear system is a nontrivial task [1]. Even in two and three dimensions a lot of work has to be done. We will demonstrate two different realizations. The first approach (see [3]) is based on Java, Java3D, and the BigRational package. The 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 [2]) uses Maple and intpakX 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 rho (|I- mid(A)*A|) < 1. Here I means the identity matrix, mid(A) denotes the midpoint matrix and rho denotes the spectral radius of a real matrix.

[1] G. Alefeld, G. Mayer: On the symmetric and unsymmetric solution set of interval systems. SIAM J. Matrix Anal. Appl., Vol. 16, 1995.

[2] S. Braun: Visualisierung der exakten Loesungsmengen von linearen Intervallgleichungssystemen in Maple, Bachelor-Thesis, University of Wuppertal, 2006.

[3] G. Paw: Ein intuitiv bedienbares Java-Applet zur Visualisierung exakter Lösungsmengen von mengenwertigen numerischen Problemen. Bachelor-Thesis, University of Wuppertal, 2006.