Abstract
In this paper new factorization techniques for computation of the operational space mass matrix (/spl Lambda/) and its inverse (/spl Lambda//sup -1/) are developed. Starting with a new factorization of the inverse of mass matrix (M/sup -1/) in the form of Schur complement as M/sup -1/=C-B/sup T/A/sup -1/B, where A and B are block tridiagonal matrices and C is a tridiagonal matrix, similar factorizations for /spl Lambda/ and /spl Lambda//sup -1/ are derived. Specifically, the Schur complement factorizations of /spl Lambda//sup -1/ and /spl Lambda/ are derived as /spl Lambda//sup -1/=D-E/sup T/A/sup -1/E and /spl Lambda/=G-R/sup T/S/sup -1/R, where E and R are sparse matrices and D and G are 6/spl times/6 matrices. The Schur complement factorization provides a unified framework for computation of M/sup -1/, /spl Lambda//sup -1/, and /spl Lambda/. The main advantage of these new factorizations is that they are highly efficient for parallel computation. With O(N) processors, the computation of /spl Lambda//sup -1/ and /spl Lambda/ as well as their operator applications can be performed in O(log N) steps.<>