1 Application of the asynchronous iterative methods to construct a processor V. Beletsky*, A. Chemeris** * Technical Univercity of Szczecin ** The Institute of Problems of Simulation in Power Engineering The Ukrainian National Academy of Sciences 15, General Naumov st., 164, Kiev 252680, Ukraine e-mail: chemeris@sabbo.net Abstract The asynchronous iterative method are considered to design the arithmetic units for the solution of the one-dimensioned equation f(x) = a with a feedback path over the digital units. The convergence conditions and the method error are presented. As an example the divider has been considered and the table of testing results has been done. Keywords : iterative methods, asynchronous devices, combinational logic, convergence of the method, arithmetic unit. Introduction A lot of iterative methods were elaborated for the solution of algebraic and transcendental equations f(x) = a . The main idea of this methods is to build the function φ(x) so that the searching root x=x * has to be the root of the equation x = φ(x) . Then one builds the sequence {x (k) } using the equation x (k) =φ(x (k-1) ), k=0..n . The sequence {x (k) } converges at the interval J to the single root x=x * if the function φ(x) satisfies Lipshitz condition | φ(r) - φ(q) | ≤ L|r - q|; 0 ≤ L < 1; r,q ∈ Y. (1)