Paper Info
Title
Direct and iterative methods for interval parametric algebraic systems producing parametric solutions.
Abstract
This paper deals with interval parametric linear systems with general dependencies. Motivated by the so-called parameterized solution introduced by Kolev, we consider the enclosures of the solution set in a revised affine form. This form is advantageous to a classical interval solution because it enables us to obtain both outer and inner bounds for the parametric solution set and, thus, intervals containing the endpoints of the hull solution, among others. We propose two solution methods, a direct method called the generalized expansion method and an iterative method based on interval-affine Krawczyk iterations. For the iterative method, we discuss its convergence and show the respective sufficient criterion. For both methods, we perform theoretical and numerical comparisons with some other approaches. The numerical experiments, including also interval parametric linear systems arising in practical problems of structural and electrical engineering, indicate the great usefulness of the proposed methodology and its superiority over most of the existing approaches to solving interval parametric linear systems.
Year
DOI
Venue
2019
10.1002/nla.2229
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
Keywords
DocType
Volume
affine arithmetic,interval computation,linear equations,parametric system
Journal
26.0
Issue
ISSN
Citations 
3.0
1070-5325
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Iwona Skalna14212.22
Milan Hladík226836.33