Argyros, Ioannis K.George, SanthoshRegmi, SamundraArgyros, Christopher I.2024-04-262024-04-262024-04-10Algorithms 17 (4): 154 (2024)https://hdl.handle.net/10657/17058Iterative algorithms requiring the computationally expensive in general inversion of linear operators are difficult to implement. This is the reason why hybrid Newton-like algorithms without inverses are developed in this paper to solve Banach space-valued nonlinear equations. The inverses of the linear operator are exchanged by a finite sum of fixed linear operators. Two types of convergence analysis are presented for these algorithms: the semilocal and the local. The Fréchet derivative of the operator on the equation is controlled by a majorant function. The semi-local analysis also relies on majorizing sequences. The celebrated contraction mapping principle is utilized to study the convergence of the Krasnoselskij-like algorithm. The numerical experimentation demonstrates that the new algorithms are essentially as effective but less expensive to implement. Although the new approach is demonstrated for Newton-like algorithms, it can be applied to other single-step, multistep, or multipoint algorithms using inverses of linear operators along the same lines.2024-04-26