The paper concerns efficient parallel computation methods for solving matrix linear equations using the preconditioned conjugate gradient method. Efficient parallelization methods of the preconditioner module have been proposed based on execution in a special architecture of dynamically reconfigurable shared memory clusters. The assumed system is provided with a novel efficient inter-processor communication technique called ?communication on the fly?, which is very suitable for fine grain parallel computations. Two-step parallel data decomposition is implemented in the elaborated preconditioner, which leads to the decrease of computation grain and overlapping of communication with computations. Comparative experimental results are presented of program execution efficiency in a standard distributed multicomputer cluster based on message passing and in the architecture of dynamic SMP clusters with the communication on the fly.