ABS methods for nonlinear systems of algebraic equations

Articolo di rassegna dei risultati classici sui metodi ABS per sistemi algebrici nonlineari e discussione di nuove applicazioni a problemi strutturati, in particolare nascenti dal metodo primale-duale interior point per il problema LP.We consider on application of the ABS procedure to the linear systems arising from the primal-dual interior point method where Newton methods is used to compute a path to the solution. When approaching the solution the linear system, which has the form of normal equations of the second kind, becomes more and more ill conditioned. We show how the use of the Huang algorithm in the ABS class can reduce the ill conditioning. Preliminary numerical experiments show that the proposed approach can provide a residual in the computed solution up to sixteen orders lower