Preconditioning for Sparse Linear Systems at the Dawn of the 21st Century : History, Current Developments, and Future Perspectives
Author
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-49, 49 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-12-26
Country of Publication
Egypt
No. of Pages
49
Main Subjects
Abstract EN
Iterative methods are currently the solvers of choice for large sparse linear systems of equations.
However, it is well known that the key factor for accelerating, or even allowing for, convergence is the preconditioner.
The research on preconditioning techniques has characterized the last two decades.
Nowadays, there are a number of different options to be considered when choosing the most appropriate preconditioner for the specific problem at hand.
The present work provides an overview of the most popular algorithms available today, emphasizing the respective merits and limitations.
The overview is restricted to algebraic preconditioners, that is, general-purpose algorithms requiring the knowledge of the system matrix only, independently of the specific problem it arises from.
Along with the traditional distinction between incomplete factorizations and approximate inverses, the most recent developments are considered, including the scalable multigrid and parallel approaches which represent the current frontier of research.
A separate section devoted to saddle-point problems, which arise in many different applications, closes the paper.
American Psychological Association (APA)
Ferronato, Massimiliano. 2012. Preconditioning for Sparse Linear Systems at the Dawn of the 21st Century : History, Current Developments, and Future Perspectives. ISRN Applied Mathematics،Vol. 2012, no. 2012, pp.1-49.
https://search.emarefa.net/detail/BIM-447829
Modern Language Association (MLA)
Ferronato, Massimiliano. Preconditioning for Sparse Linear Systems at the Dawn of the 21st Century : History, Current Developments, and Future Perspectives. ISRN Applied Mathematics No. 2012 (2012), pp.1-49.
https://search.emarefa.net/detail/BIM-447829
American Medical Association (AMA)
Ferronato, Massimiliano. Preconditioning for Sparse Linear Systems at the Dawn of the 21st Century : History, Current Developments, and Future Perspectives. ISRN Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-49.
https://search.emarefa.net/detail/BIM-447829
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-447829