  Recomi (REpeated COrrelation Matrix Inversion) is a polynomially fast
algorithm for searching optimally stable solutions of the perceptron learning
problem. For random unbiased and biased patterns it is shown that the algorithm
is able to find optimal solutions, if any exist, in at worst O(N^4) floating
point operations. Even beyond the critical storage capacity alpha_c the
algorithm is able to find locally stable solutions (with negative stability) at
the same speed. There are no divergent time scales in the learning process. A
full proof of convergence cannot yet be given, only major constituents of a
proof are shown.
