To overcome these drawbacks, Noor [2, 3] used the technique of updating the solution to suggest the two-step (or predictor-corrector) method for solving the variational inequality (1.2).
In 2000, Noor [9] first introduced a three-step iterative sequence and studied the approximate solutions of variational inclusion in Hilbert spaces by using the techniques of updating the solution and the auxiliary principle.
In recent years, much attention have been given to develop a class of two-step and three-step iterative methods for solving the variational inclusions and inequalities using the technique of updating the solution.
In each iteration, the column of Λ having the highest correlation with the error vector is selected and is used to update the approximate solution of R. The iterative process will not be stopped until the error is small enough or the number of iterations is equal to V. In detail, the process of signal reconstruction through OMP method can be described as follows: Initialization.
The position and velocities of each particle is next updated based on the solution of the classical equation of motion [21].
The PJD algorithm is a subspace method, which extracts the candidate eigenpair from a search space and the space updated by embedding the solution of the correction equation at the JD iteration.
We design, analyse and test a class of incomplete orthogonal factorization preconditioners constructed from Givens rotations, incorporating some dropping strategies and updating tricks, for the solution of large sparse systems of linear equations.
At each time step, the method consists of two stages to update the new solution.
(ii) Iteration : update by finding the solution of KKT condition of (C.2) with respect to ; find and, such that and,.
Afterwards, the correction function is updated until convergence to the solution of the original non-linear equation is achieved.
