A very rapidly convergent iterative method for parallel inversion of matrices

A very fast iterative method is presented, for the inversion of matrices of the form A=I-P, where P is a convergent matrix. The method is well suitable for parallel implementation. The convenient number of iterations required is the logarithm of the number of iterations required by a classical iterative method applied to the splitting I-P of the matrix. Asimpotically, the method requires C(log n A(logn log log n)) steps on n^3 processors, where a(p) is the complexity of the arithmetic operations with p digits. Further, a detailed study of the total complexity for finite values of n shows the relations among the number of steps, the spectral radius and the dimension of the matrix.