An asynchronous direct solver for banded linear systems

An asynchronous direct solver for banded linear systems Banded linear systems occur frequently in mathematics and physics. However, direct solvers for large systems cannot be performed in parallel without communication. The aim of this paper is to develop a general asymmetric banded solver with a direct approach that scales across many processors efficiently. The key mechanism behind this is that reduction to a row-echelon form is not required by the solver. The method requires more floating point calculations than a standard solver such as LU decomposition, but by leveraging multiple processors the overall solution time is reduced. We present a solver using a superposition approach that decomposes the original linear system into q subsystems, where q is the number of superdiagonals. These methods show optimal computational cost when q processors are available because each system can be solved in parallel asynchronously. This is followed by a q×q dense constraint matrix problem that is solved before a final vectorized superposition is performed. Reduction to row echelon form is not required by the solver, and hence the method avoids fill-in. The algorithm is first developed for tridiagonal systems followed by an extension to arbitrary banded systems. Accuracy and performance is compared with existing solvers and software is provided in the supplementary material. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerical Algorithms Springer Journals

An asynchronous direct solver for banded linear systems

Loading next page...
 
/lp/springer_journal/an-asynchronous-direct-solver-for-banded-linear-systems-uW2OOih5CU
Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media New York (outside the USA)
Subject
Computer Science; Numeric Computing; Algorithms; Algebra; Theory of Computation; Numerical Analysis
ISSN
1017-1398
eISSN
1572-9265
D.O.I.
10.1007/s11075-016-0251-3
Publisher site
See Article on Publisher Site

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 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

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

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial