# Computing and Visualizing Solution Sets of Interval Linear Systems

Serdica Journal of Computing (2007)

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

## Access Full Article

top## Abstract

top## How to cite

topKrämer, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.