Triangular factorization of inverse data covariance matrices

A novel Cholesky factorization of the inverse covariance matrix is described which can be performed with fully parallel matrix-vector operations, instead of more costly back substitutions. This factorization reformulates the Sherman-Morrison-Woodbury matrix inverse identity as a downdating problem. Givens rotations provide triangularized factors of the inverse data covariance matrix, and the final adaptive solution is obtained after two triangular matrix-vector products. This novel factorization algorithm operates in the voltage (or square root) domain to maintain the numerical robustness of earlier factorization techniques. Simulation results show that this algorithm is highly stable and can yield more accurate results at lower processor precision