In the paper, the optimal self-scaling strategy to the modified symmetric rank one (HSR1) update, which satisfies the modified quasi-Newton equation, is derived to improve the condition number of the updates. The scaling factors are derived from minimizing the estimate of upper bounds on the condition number of the updating matrix. Theoretical analysis, and numerical experiments and comparisons show that introducing the optimal scaling factor into the modified symmetric rank one update preserves the positive definiteness of updates, and greatly improves the stability and numerical performance of the modified symmetric rank one algorithm.

Objective To study the antitumor activities of RRx-001 derivatives with novel covalent fragments. Methods Four targeted compounds were designed and synthesized. The structures were confirmed by ¹H NMR and HRMS. A549 and HCT116 cancer cell lines were selected for antiproliferative activity assays. Results All the compounds revealed antitumor activities and compound ZM528 showed the best antitumor activity against these two cell lines with IC₅₀ values of （5.1±4.8） μmol/L and （6.0±2.7） μmol/L, respectively. Conclusion The result indicated that bromoacetyl group of RRx-001 could be substituted with other covalent fragments.