Jacobi and Gauss-Seidel Iterations for Polytopic Systems: Convergence via Convex M-Matrices

Jacobi and Gauss-Seidel Iterations for Polytopic Systems: Convergence via Convex M-Matrices A natural generalization of the Jacobi and Gauss-Seidel iterations for interval systems is to allow the matrices to reside in convex polytopes. In order to apply the standard convergence criteria involving M-matrices to iterations for polytopic systems, we derive conditions for a convex polytope of matrices to be a polytope of M-matrices in terms of its vertices. We show the conditions are used in the convergence analysis of iterations for block and nonlinear polytopic systems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Jacobi and Gauss-Seidel Iterations for Polytopic Systems: Convergence via Convex M-Matrices

Loading next page...
 
/lp/springer_journal/jacobi-and-gauss-seidel-iterations-for-polytopic-systems-convergence-csqtrQ1Yni
Publisher
Springer Journals
Copyright
Copyright © 2000 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009961021112
Publisher site
See Article on Publisher Site

Abstract

A natural generalization of the Jacobi and Gauss-Seidel iterations for interval systems is to allow the matrices to reside in convex polytopes. In order to apply the standard convergence criteria involving M-matrices to iterations for polytopic systems, we derive conditions for a convex polytope of matrices to be a polytope of M-matrices in terms of its vertices. We show the conditions are used in the convergence analysis of iterations for block and nonlinear polytopic systems.

Journal

Reliable ComputingSpringer Journals

Published: Oct 7, 2004

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off