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