Triangular Factorization and Inversion by Fast Matrix Multiplication
James R. Bunch, John E. Hopcroft · Mathematics of Computation · 1974
The fast matrix multiplication algorithm by Strassen is used to obtain the triangular factorization of a permutation of any nonsingular matrix of order n in $< {C_1}{n^{{{\log }_2}7}}$ operations, and, hence, the inverse of any nonsingular matrix in $< {C_2}{n^{{{\log }_2}7}}$ operations.