James W. Demmel and Fritz Kruckeberg

EECS Department, University of California, Berkeley

Technical Report No. UCB/CSD-83-126

1983

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.

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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},
    Year= {1983},
    Month= {Jul},
    Url= {http://www2.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://www2.eecs.berkeley.edu/Pubs/TechRpts/1983/5455.html
%F Demmel:CSD-83-126