Algorithmes de calcul du maximum des formes quadratiques sur la boule unité de la norme du max (Q788458)

Some direct and indirect methods are studied for computing \(Max\{x^ tAx,\phi_{\infty}(x)\leq 1\}\). Direct methods are constructed using particular properties of \(\phi_ 1,\phi_ 2,\phi_{\infty}\) norms. These methods are very simple, but uniquely suitable to certain families of matrices. The indirect method is the selfdual method, introduced by the author [Iterative methods for computing the bound norm of matrices. (Linear Alg. and Its Appl.; to appear) and Contribution à la théorie de normes et ses applications à l'analyse numérique. Doctoral thesis (1981). Université Scientifique et Médicale de Grenoble.] with \(\phi =\phi_ 1\). In this case the problem of choosing an initial vector so that convergence of the iterative sequence occurs to an optimal solution is largely discussed.