Generalized matrix inversion is not harder than matrix multiplication

Starting from the Strassen method for rapid matrix multiplication and inversion as well as from the recursive Cholesky factorization algorithm, we introduced a completely block recursive algorithm for generalized Cholesky factorization of a given symmetric, positive semi-definite matrix A∈R^n×n$A\in {\mathbb{R}}^{n\times n}$. We used the Strassen method for matrix inversion together with the recursive generalized Cholesky factorization method, and established an algorithm for computing generalized {2,3}$\{2,3\}$ and {2,4}$\{2,4\}$ inverses. Introduced algorithms are not harder than the matrix–matrix multiplication.