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ELA

AN ALGORITHM FOR SOLVING THE ABSOLUTE VALUE

EQUATION

∗

JIRI ROHN†

Abstract. Presented is an algorithm which for eachA, B∈Rn×n

andb∈Rn

in a finite number of steps either finds a solution of the equationAx+B|x|=b, or states existence of a singular matrix Ssatisfying|S−A| ≤ |B|(and in most cases also constructs such anS).

Key words. Absolute value equation, Algorithm, Regularity, Singularity, Theorem of the alternatives.

AMS subject classifications.15A06, 65H10, 90C33.

∗Received by the editors March 10, 2009. Accepted for publication August 27, 2009. Handling

Editor: Daniel Szyld.

†Institute of Computer Science, Czech Academy of Sciences, Prague, and School of Business

Ad-ministration, Anglo-American University, Prague, Czech Republic ([email protected]). Supported by the Czech Republic Grant Agency under grants 201/09/1957 and 201/08/J020, and by the Institu-tional Research Plan AV0Z10300504.

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 18, pp. 589-599, September 2009

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