en Other Other پژوهشی Original <p align="center"> <span style="FONT-SIZE: 14pt FONT-FAMILY: Mitra mso-fareast-font-family: 'Times New Roman' mso-fareast-language: EN-US mso-ascii-font-family: Mitra mso-hansi-font-family: Mitra mso-ansi-language: EN-US mso-bidi-language: FA">Abstract</span></p><p><font face="georgia,times new roman,times,serif">  We consider an application of the ABS procedure to the linear systems arising from the primal-dual interior point methods where Newton method is used to compute 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.</font></p> ABS methods, normal equations of the second kind,Huang algorithm, primal-dual interior point method, Newton method 28 34 http://iors.ir/journal/browse.php?a_code=A-10-6-5&slc_lang=en&sid=1 Emilio Spedicato emilio@unibg.it 000319475328460035 000319475328460035 Yes Department of Mathematics, University of Bergamo, Bergamo, Italy Marco Bonomi 000319475328460036 000319475328460036 No Department of Mathematics, University of Bergamo, Bergamo, Italy Antonino Del Popolo 000319475328460037 000319475328460037 No Department of Mathematics, University of Bergamo, Bergamo, Italy