Hyperbolic updating of LDU decompositions
Edward J. Baranoski · 2002
Presents a new hyperbolic householder algorithm to efficiently update and downdate the LDU decomposition of covariance matrices. While useful in its own right, this is a powerful tool when combined with Sylvester's law of inertia, which equates the number of positive (negative) eigenvalues of a matrix with the number of positive (negative) numbers in the diagonal matrix of the LDU decomposition. This allows the hyperbolic LDU updating procedure to be used to track the eigenvalue structure of a set of data vectors. An example application is presented which tracks the number of sources present in a set of array data vectors using a block averaging technique.>