Gradient methods for computing the Drazin-inverse solution

• Autores: Sladjana Miljkovic, Marko Miladinovic, Predrag S. Stanimirovic, Yimin Wei
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 253, Nº 1, 2013, págs. 255-263
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.04.030
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• Resumen

  • The problem of computing the vector ADb, in the cases when it provides a solution of a singular linear system, is reduced to the problem of finding a least-squares solution of an appropriate linear system. Later the presented ideas are extended to arbitrary linear systems. As a consequence, we present iterative methods for computing the vector ADb in general. The functionality of the exposed algorithms is based on a specific representation of the Drazin-inverse solution, as well as the properties that we introduce. Convergence results of the proposed methods are also considered. Illustrative numerical examples are presented.