Title :
Hyperbolic updating of LDU decompositions
Author :
Baranoski, Edward J.
Author_Institution :
Lincoln Lab., MIT, Lexington, MA, USA
Abstract :
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
Keywords :
array signal processing; covariance matrices; eigenvalues and eigenfunctions; matrix decomposition; LDU decompositions; Sylvester´s law of inertia; array data vectors; block averaging; covariance matrices; data vectors; diagonal matrix; eigenvalue structure; eigenvalues; hyperbolic householder algorithm; updating procedure; Architecture; Contracts; Covariance matrix; Eigenvalues and eigenfunctions; Interference; Laboratories; Matrix decomposition; Monitoring; Power capacitors; Voltage;
Conference_Titel :
Digital Signal Processing Workshop, 1994., 1994 Sixth IEEE
Conference_Location :
Yosemite National Park, CA
Print_ISBN :
0-7803-1948-6
DOI :
10.1109/DSP.1994.379822
