Influences of Rounding Errors in Solving Large Sparse Linear Systems

Axel Facius ()
Additional contact information
Axel Facius: Universität Karlsruhe (TH), Institut für Angewandte Mathematik

A chapter in Developments in Reliable Computing, 1999, pp 17-30 from Springer

Abstract: Abstract In many research areas like structural mechanics, economics, meteorology, and fluid dynamics, problems are mapped to large sparse linear systems via discretization. The resulting matrices are often ill-conditioned with condition numbers of about 1016 and higher. Usually these systems are preconditioned before they are fed to an iterative solver. Especially for ill-conditioned systems, we show that we have to be careful with these three classical steps — discretization, preconditioning, and (iterative) solving. For Krylov subspace solvers we give some detailed analysis and show possible improvements based on a multiple precision arithmetic. This special arithmetic can be easily implemented using the exact scalar product — a technique for computing scalar products of floating point vectors exactly.

Keywords: High precision arithmetic; discretization; preconditioning; Krylov subspace methods; large sparse linear systems (search for similar items in EconPapers)
Date: 1999
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-1247-7_2

Ordering information: This item can be ordered from
http://www.springer.com/9789401712477

DOI: 10.1007/978-94-017-1247-7_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().