Guaranteed Convergence Rate Estimates for a Class of Iterative Procedures: Their Comparison

The main difficulty in parallelization and synchronization of computations for speeding up the convergence of iterative procedures is the optimal guaranteed convergence rate estimation. A theorem is formulated concerning the guaranteed convergence rate estimates for certain procedures, in which resources are primarily allotted to the computation of nonlinearity components. Its proof is based on the use of new estimates for the spectral radii of the products of matrix sequences of asynchronous component computations.