Iterative method for solving linear operator equation of the first kind

In this work, we study the iterative method for solving linear operator equation of the first kind. We present a new version of method based on the applied the iterative performance on the modified Lavrentiev method. This method is used to resolve a linear operator problem of the first kind. The suggested iterative can used to compute approximate solutions with high quality than the (standard) modified Lavrentiev regularization method. We also compared the new iterative method (modified Lavrentiev) with Landweber iterative method. The numerical testing shows the efficiency of the new iterative method in its application to resolve the inverse heat equation when trying to find the boundary value function. •Studying of new iteration algorithm and mathematical experimentations show the efficiency of the new iteration method.•Iteration method is depended on decomposed the main linear operator by using polar decomposition in order to obtain unitary operator.•The new unitary operator increases the convergence of iteration.