A parallel implementation of the matrix cross approximation method

The matrix cross approximation method is a fast method based on low-rank matrix approximations with complexity $O((m+n)r^2)$ arithmetic operations. Its main feature consists in the following: if a matrix is not given as an array but is given as a function of two integer arguments, then this method allows one to compute the low-rank approximation of the given matrix by evaluating only $O((m+n)r)$ values of this function. However, if the matrix is extremely large or the evaluation of its elements is computationally expensive, then such an approximation becomes timeconsuming. For such cases, the performance of the method can be improved via parallelization. In this paper we propose an efficient parallel algorithm for the case of an equal computational cost for the evaluation of each matrix element.