Two Iterative Methods for Solving Linear Interval Systems
Joint Authors
Siahlooei, Esmaeil
Shahzadeh Fazeli, Seyed Abolfazl
Source
Applied Computational Intelligence and Soft Computing
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-10-08
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Information Technology and Computer Science
Abstract EN
Conjugate gradient is an iterative method that solves a linear system Ax=b, where A is a positive definite matrix.
We present this new iterative method for solving linear interval systems Ãx̃=b̃, where à is a diagonally dominant interval matrix, as defined in this paper.
Our method is based on conjugate gradient algorithm in the context view of interval numbers.
Numerical experiments show that the new interval modified conjugate gradient method minimizes the norm of the difference of Ãx̃ and b̃ at every step while the norm is sufficiently small.
In addition, we present another iterative method that solves Ãx̃=b̃, where à is a diagonally dominant interval matrix.
This method, using the idea of steepest descent, finds exact solution x̃ for linear interval systems, where Ãx̃=b̃; we present a proof that indicates that this iterative method is convergent.
Also, our numerical experiments illustrate the efficiency of the proposed methods.
American Psychological Association (APA)
Siahlooei, Esmaeil& Shahzadeh Fazeli, Seyed Abolfazl. 2018. Two Iterative Methods for Solving Linear Interval Systems. Applied Computational Intelligence and Soft Computing،Vol. 2018, no. 2018, pp.1-13.
https://search.emarefa.net/detail/BIM-1117045
Modern Language Association (MLA)
Siahlooei, Esmaeil& Shahzadeh Fazeli, Seyed Abolfazl. Two Iterative Methods for Solving Linear Interval Systems. Applied Computational Intelligence and Soft Computing No. 2018 (2018), pp.1-13.
https://search.emarefa.net/detail/BIM-1117045
American Medical Association (AMA)
Siahlooei, Esmaeil& Shahzadeh Fazeli, Seyed Abolfazl. Two Iterative Methods for Solving Linear Interval Systems. Applied Computational Intelligence and Soft Computing. 2018. Vol. 2018, no. 2018, pp.1-13.
https://search.emarefa.net/detail/BIM-1117045
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1117045