Moore Penrose inverse for row or column symmetric matrix

The problem of fast computing the Moore Penrose inverse of row or column symmetric(matrix) is condidered.Two new algorithms based on a correspondence of Moore Penrose inverse(matrices) between the row or column symmetric matrix and its mother matrix are obtained.Theoretical analysis and numerical evidence show that,for a class of row or column symmetric matrices,using the mother matrix rather than the row or column symmeric matrix per se can save dramatically the CPU time and memory without loss of any numerical precision,when computing the Moore Penrose(inverse).