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On Unique Solvability of the Absolute Value Equation
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SYSNO ASEP 0328409 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On Unique Solvability of the Absolute Value Equation Title Jednoznačná řešitelnost rovnice s absolutní hodnotou Author(s) Rohn, Jiří (UIVT-O) SAI, RID, ORCID Source Title Optimization Letters. - : Springer - ISSN 1862-4472
Roč. 3, č. 4 (2009), s. 603-606Number of pages 4 s. Language eng - English Country DE - Germany Keywords absolute value equation ; unique solution ; singular values Subject RIV BA - General Mathematics R&D Projects GA201/09/1957 GA ČR - Czech Science Foundation (CSF) GC201/08/J020 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000268445100013 DOI 10.1007/s11590-009-0129-6 Annotation It is proved that the singular value condition $\sigma_{\max}(|B|)<\sigma_{\min}(A)$ implies unique solvability of the absolute value equation $Ax+B|x|=b$ for each right-hand side $b$.. This is a generalization of an earlier result by Mangasarian and Meyer proved for the special case of $B=-I$. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2010
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