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Title: Computing and Visualizing Solution Sets of Interval Linear Systems
Authors: Krämer, Walter
Keywords: Solution Sets
Interval Linear Systems
Reliable Computations
Visualization Using Computer Algebra Tools
Issue Date: 2007
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Journal of Computing, Vol. 1, No 4, (2007), 455p-468p
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.
Description: The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006
ISSN: 1312-6555
Appears in Collections:Volume 1 Number 4

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