A new method, the Dynamical Systems Method (DSM), justified recently, is applied to solving ill-conditioned linear algebraic system (ICLAS). The DSM gives a new approach to solving a wide class of ill-posed problems. In this paper a new iterative scheme for solving ICLAS is proposed. This iterative scheme is based on the DSM solution. An a posteriori stopping rules for the proposed method is ju...

By exploiting the idea employed in spectral Dai-Yuan method by Xue et al. [IEICE Trans. Inf. Syst. 101 (12)2984-2990 (2018)] and approach applied modified Hager-Zhang scheme for nonsmooth optimization [PLos ONE 11(10): e0164289 (2016)], we develop a type iterative convex constrained nonlinear monotone system. The scheme's algorithm is obtained combining its search direction with projection [Klu...

We prove results concerning data dependence of Noor and SP iterative schemes using certain quasi-contractive operators in real Banach spaces. Our results reveal that by choosing an approximate quasi-contractive operator (for which it is possible to compute the fixed point); we can approximate the fixed point of the given operator. An example is also provided to explain the validity of our results.

In this paper we propose and studied a new composite iterative scheme with certain control con-ditions for viscosity approximation for a zero of accretive operator and xed points problems in areflexive Banach space with weakly continuous duality mapping. Strong convergence of the sequencefxng dened by the new introduced iterative sequence is proved. The main results improve andcomplement the co...