Adaptive Wegstein method for a coefficient inverse problem for one model of HIV infection

We consider a coefficient inverse problems for one model of HIV infection. The problem is formulated as an minimization problem of a quadratic residual functional. The last one is turned to the fixed point problem. We study two approaches to obtaining approximations such as the adaptive Wegstein method to solutions of the fixed point problem. One way is the vector approach, this method uses the ratio of the norms of residuals for finding parameters of the method. The other way is the componentwise approach that shift tracking of approximations in each coordinate more subtle. Numerical results are presented. 1 Adaptive Wegstein method for fixed point problem There are an impressive number of methods for the approximate solutions of nonlinear scalar equations and systems. The search for new methods of solving such equations and ways to improve the efficiency of the wellknown and practically proven methods remains important. Newton’s method and simple iterations method, being the simplest to build and structure and most capable of an exhaustive study, often serve as the starting point for this. One way to improve the convergence and extend the scope of applicability of linearly convergent iterative processes is to build processes of the Fejer type [1] which are called Mann iterations (see [2, 3, etc.]). Suppose that the problem of a fixed point is defined by the equality