Combining the preconditioned conjugate gradient method and a matrix iterative method (Q1915630)

The aim of this paper is to study the preconditioned conjugate gradient method with a special choice of the initial approximation of the solution for solving systems of linear equations with symmetric and positive definite coefficient matrices. The initial approximation of the solution is constructed as a result of a matrix iteration method. The author shows that a relatively small number of successive iterations is enough for starting the conjugate gradients. For the demonstration of the new algorithm and the presented theoretical results two numerical examples are included.