Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

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