Solution Sets Interval Linear Systems Reliable Computations Visualization Using Computer Algebra Tools intpakX
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
