An automatic scheḿe for updafing the block size in the block conjugate gradient method for solving linear systems

The paper considers the problem of constructing on efficient automatic procedure for reducing the block size in the block conjugate gradient method providing for the rate of convergence comparable with that of the block conjugate gradient method with constant block size. Results of numerical experiments show that, independently of the type of distribution of the smallest eigenvalues of the preconditioned matrix, the procedure suggested always leads to a decrease of arithmetic costs with respect to those of the block method with constant block size.