A verification method for enclosing solutions of absolute value equations

• Autores: Haijun Wang, Hao Liu, Suyu Cao
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 64, Fasc. 1, 2013, págs. 17-38
• Idioma: inglés
• DOI: 10.1007/s13348-011-0057-5
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• Resumen

  • In this paper, we investigate the NP-hard absolute value equations (AVE) Ax − |x| = b and establish two computational enclosures for the solution of AVE. The condition for enclosing the solution and guaranteeing the existence of solutions of AVE is presented in a given domain. Based on this condition, new algorithms are designed to compute an interval to enclose the unknown solution of AVE. Numerical results are reported to support the theoretical analysis in the paper.