Liesen, JörgTichý, Petr2017-12-192017-12-192009-07-300895-4798https://depositonce.tu-berlin.de/handle/11303/7286http://dx.doi.org/10.14279/depositonce-6559We show that certain matrix approximation problems in the matrix 2-norm have uniquely defined solutions, despite the lack of strict convexity of the matrix 2-norm. The problems we consider are generalizations of the ideal Arnoldi and ideal GMRES approximation problems introduced by Greenbaum and Trefethen [SIAM J. Sci. Comput., 15 (1994), pp. 359–368]. We also discuss general characterizations of best approximation in the matrix 2-norm and provide an example showing that a known sufficient condition for uniqueness in these characterizations is not necessary.en515 Analysis512 Algebramatrix approximation problemspolynomials in matricesmatrix functionsmatrix 2-normGMRESArnoldi’s methodArticle1095-7162