# An Interval Algorithm for Solving Systems of Linear Equations to Prespecified Accuracy

### James W. Demmel and Fritz Kruckeberg

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-83-126

July 1983

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1983/CSD-83-126.pdf

We describe an interval arithmetic algorithm for solving a special class of simultaneous linear equations. This class includes but is not limited to systems
*Ax*=
*b* where
*A* and
*b* have integer entries. The algorithm uses fixed point arithmetic, and has two properties which distinguish it from earlier algorithms: given the absolute accuracy
*e* desired, the algorithm uses only as much precision as needed to achieve it, and the algorithm can adjust its own parameters to minimize computation time.

BibTeX citation:

@techreport{Demmel:CSD-83-126, Author = {Demmel, James W. and Kruckeberg, Fritz}, Title = {An Interval Algorithm for Solving Systems of Linear Equations to Prespecified Accuracy}, Institution = {EECS Department, University of California, Berkeley}, Year = {1983}, Month = {Jul}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1983/5455.html}, Number = {UCB/CSD-83-126}, Abstract = {We describe an interval arithmetic algorithm for solving a special class of simultaneous linear equations. This class includes but is not limited to systems <i>Ax</i>=<i>b</i> where <i>A</i> and <i>b</i> have integer entries. The algorithm uses fixed point arithmetic, and has two properties which distinguish it from earlier algorithms: given the absolute accuracy <i>e</i> desired, the algorithm uses only as much precision as needed to achieve it, and the algorithm can adjust its own parameters to minimize computation time.} }

EndNote citation:

%0 Report %A Demmel, James W. %A Kruckeberg, Fritz %T An Interval Algorithm for Solving Systems of Linear Equations to Prespecified Accuracy %I EECS Department, University of California, Berkeley %D 1983 %@ UCB/CSD-83-126 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1983/5455.html %F Demmel:CSD-83-126