By Topic

Solving triangular linear systems in parallel using substitution

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Santos, E.E. ; Div. of Comput. Sci., California Univ., Berkeley, CA, USA

Working within the LogP model, we present parallel triangular solvers which use forward/backward substitution and show that they are optimal. We begin by deriving several lower bounds on execution time for solving triangular linear systems. Specifically, we derive lower bounds in which it is assumed that the number of data items per processor is bounded, a general lower bound, and lower bounds for specific data layouts commonly used for this problem. Furthermore, algorithms are provided which have running times within a constant factor of the lower bounds described. One interesting result is that the popular 2-dimensional block matrix layout necessarily results in significantly longer running times than simpler one-dimensional schemes. Finally, we present a generalization of the lower bounds to banded triangular linear systems

Published in:

Parallel and Distributed Processing, 1995. Proceedings. Seventh IEEE Symposium on

Date of Conference:

25-28 Oct 1995