Introducing One Step Back Iterative Approach to Solve Linear and Non Linear Fixed Point Problem
For researchers working on iterative methods for fixed-point problems, this is an incremental contribution that modifies existing coordinate descent ideas.
The paper introduces a new iterative method, the one step back approach, which anticipates the consequences of iterative computation per coordinate to optimize coordinate selection. It demonstrates the method on linear and nonlinear fixed-point problems.
In this paper, we introduce a new iterative method which we call one step back approach: the main idea is to anticipate the consequence of the iterative computation per coordinate and to optimize on the choice of the sequence of the coordinates on which the iterative update computations are done. The method requires the increase of the size of the state vectors and one iteration step loss from the initial vector. We illustrate the approach in linear and non linear iterative equations.