# Computing and Visualizing Solution Sets of Interval Linear Systems

• Volume: 1, Issue: 4, page 455-468
• ISSN: 1312-6555

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## Abstract

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The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006The 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.

## How to cite

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Krämer, Walter. "Computing and Visualizing Solution Sets of Interval Linear Systems." Serdica Journal of Computing 1.4 (2007): 455-468. <http://eudml.org/doc/11436>.

@article{Krämer2007,
abstract = {The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006The 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.},
author = {Krämer, Walter},
journal = {Serdica Journal of Computing},
keywords = {Solution Sets; Interval Linear Systems; Reliable Computations; Visualization Using Computer Algebra Tools; intpakX; solution sets; interval linear systems; reliable computations; visualization using computer algebra tools},
language = {eng},
number = {4},
pages = {455-468},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Computing and Visualizing Solution Sets of Interval Linear Systems},
url = {http://eudml.org/doc/11436},
volume = {1},
year = {2007},
}

TY - JOUR
AU - Krämer, Walter
TI - Computing and Visualizing Solution Sets of Interval Linear Systems
JO - Serdica Journal of Computing
PY - 2007
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 1
IS - 4
SP - 455
EP - 468
AB - The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006The 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.
LA - eng
KW - Solution Sets; Interval Linear Systems; Reliable Computations; Visualization Using Computer Algebra Tools; intpakX; solution sets; interval linear systems; reliable computations; visualization using computer algebra tools
UR - http://eudml.org/doc/11436
ER -

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