Alternatives for Gaussian elimination transform and conquer algorithm

Question

Gaussian elimination algorithm in transform and conquer has O(n³) complexity. Is there any technique that give more efficient complexity of this algorithm?

Answer 1

There are algorithms for matrix inversion with better asymptotic complexity, e.g., the Strassen algorithm with complexity O(n^2.807) and the Coppersmith–Winograd algorithm with complexity O(n^2.376).

(Note that the complexity of matrix multiplication and matrix inversion are the same)