# Trading Off Parallelism and Numerical Stability

### James W. Demmel

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-92-702

September 1992

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1992/CSD-92-702.pdf

The fastest parallel algorithm for a problem may be significantly less stable numerically than the fastest serial algorithm. We illustrate this phenomenon by a series of examples drawn from numerical linear algebra. We also show how some of these instabilities may be mitigated by better floating point arithmetic.

BibTeX citation:

@techreport{Demmel:CSD-92-702, Author = {Demmel, James W.}, Title = {Trading Off Parallelism and Numerical Stability}, Institution = {EECS Department, University of California, Berkeley}, Year = {1992}, Month = {Sep}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1992/6256.html}, Number = {UCB/CSD-92-702}, Abstract = {The fastest parallel algorithm for a problem may be significantly less stable numerically than the fastest serial algorithm. We illustrate this phenomenon by a series of examples drawn from numerical linear algebra. We also show how some of these instabilities may be mitigated by better floating point arithmetic.} }

EndNote citation:

%0 Report %A Demmel, James W. %T Trading Off Parallelism and Numerical Stability %I EECS Department, University of California, Berkeley %D 1992 %@ UCB/CSD-92-702 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1992/6256.html %F Demmel:CSD-92-702