Computing and Visualizing Solution Sets of Interval Linear Systems
Serdica Journal of Computing, Tome 1 (2007) no. 4, pp. 455-468
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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.
Keywords:
Solution Sets, Interval Linear Systems, Reliable Computations, Visualization Using Computer Algebra Tools, intpakX
@article{SJC_2007_1_4_a5,
author = {Kr\"amer, Walter},
title = {Computing and {Visualizing} {Solution} {Sets} of {Interval} {Linear} {Systems}},
journal = {Serdica Journal of Computing},
pages = {455--468},
publisher = {mathdoc},
volume = {1},
number = {4},
year = {2007},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SJC_2007_1_4_a5/}
}
Krämer, Walter. Computing and Visualizing Solution Sets of Interval Linear Systems. Serdica Journal of Computing, Tome 1 (2007) no. 4, pp. 455-468. http://geodesic.mathdoc.fr/item/SJC_2007_1_4_a5/