Erratum to:

A simple derivation of the

Hansen-Bliek-Rohn-Ning-Kearfott enclosure for linear interval equations

Arnold Neumaier

Institut für Mathematik, Universität Wien Strudlhofgasse 4, A-1090 Wien, Austria

Abstract. In the Intlab program for the interval enclosure of the solution set of linear systems of equations with interval data, published in the above-mentioned paper, one rounding is in the wrong direction. A simple change amends this bug.

As observed by Helmut Jarausch (private communication), a rigorous upper bound for β_{i} in the formula (3) of the above paper, β_{i} = u_{i}/d_{i} − |b_{i}|, requires a lower bound on d_{i}. However, the program at the end of the paper provides only an upper bound (needed for α_{i}). To correct this defect, replace the line

    beta = u./d-abs(b);

in the program by

    beta=u./dlow-abs(b);

where the lower bound dlow is computed by

    dlow=v.*w-diag(B);dlow=-dlow;    % rigorous lower bound for d

to be inserted directly before the line computing

    B=B+v*w;

The work only changes by negligible O(n) operations. The corrected algorithm is available in Intlab [2].

References

[1] A. Neumaier, A simple derivation of the Hansen-Bliek-Rohn-Ning-Kearfott enclosure for linear interval equations, Reliable Computing 5 (1999), 131-136.

[2] S.M. Rump, INTLAB – INTerval LABoratory, pp. 77-104 in: Developments in reliable computing (T. Csendes, ed.), Kluwer, Dordrecht 1999.